TABLES 


or 


LOGARITHMS  OF  NUMBERS 


AND    OF 


SUES  AND  TAIGENTS 


FOR   EVERT 


TEN  SECONDS  OF  THE  QUADRANT, 


WITH  OTHER  USEFUL  TABLES. 


BY  ELIAS   LOO  MIS,  LLJX, 

PKOFESSOE   OF  NATURAL  PHILOSOPHY  AND  A8TRONOMV  IN   TALK   COLLEGE,  AND   ATTTHOK    OT 
"COTIESE   OP  MATHEMATICS." 


TWENTIETH   EDITION. 


NEW-YORK: 

HARPER   &   BROTHERS,   PUBLISHERS, 

329    &    331    PEARL    STREET, 

FRANKLIN  SQUARE. 
1862. 


Entered,  according  to  Act  of  Congress,  in  the  year  one  thousand  eight  hund  ed  and  forty-eight,  bj 

HARPER  &  BROTHERS, 
in  the  Clerk's  Office  of  the  District  Court  of  the  Southern  District  of  New  York. 


CONTENTS. 


EXPLANATION  i)P  THE  TABLES Y 

TABLE  OF  LOGARITHMS  OF  NUMBERS 1 

LOGARITHMIC  SINES  AND  TANGENTS 21 

NATURAL  SINES  AND  TANGENTS .      ....  1 16 

NATURAL  SECANTS 134 

LENGTHS  OF  CIRCULAR  ARCS 1 35 

TRAVERSE  TABLE 136 

MERIDIONAL  PARTS 142 

CORRECTIONS  TO  MIDDLE  LATITUDE 149 

LOGARITHMS  FOR  COMPOUND  INTEREST,  E^C 1 50 


PREFACE. 


THE  accompanying  tables  were  designed  to  afford  the  means  of  per 
forming  trigonometrical  computations  with  facility  and  precision.  The 
tables  chiefly  used  in  this  country  for  purposes  of  education  extend  to 
six  decimal  places,  like  those  in  the  present  collection;  but  the  pre- 
cision which  they  are  designed  to  furnish  is  only  attained  by  a  serious 
expenditure  of  labor.  In  the  Table  of  Logarithms  of  Numbers  they  do 
not  furnish  the  correction  for  a  fifth  figure  in  the  natural  number,  and 
the  labor  of  computing  this  correction  is  such  that  I  always  prefer  the 
use  of  Hutton's  Tables,  extending  to  seven  places,  even  in  computations 
to  which  six-place  logarithms  are  abundantly  competent.  In  the  pres 
ent  collection,  the  correction  for  a  fifth  figure  of  the  natural  number  is 
introduced  at  the  bottom  of  each  page,  and  the  table  is  thus  rendered 
nearly  as  useful  as  one  of  the  common  kind  extending  to  100,000.  The 
whole  has  been  carefully  compared  with  standard  authors,  and  nearly 
a  dozen  errors  have  thus  been  detected  in  the  common  tables. 

The  principal  table  in  this  collection  is  that  of  Logarithmic  Sines  and 
Tangents.  The  common  tables  in  this  country  extend  only  to  minutes, 
with  differences  to  100".  If,  in  a  trigonometrical  computation,  angles 
are  only  required  to  the  nearest  minute,  tables  to  five  places  are  quite 
sufficient ;  but  if  the  computation  is  to  be  carried  to  seconds,  these  can 
only  be  obtained  from  the  common  tables  by  a  great  expenditure  ol 
time  and  labor.  In  the  present  collection,  the  sines  and  tangents  are  fur- 
nished to  every  ten  seconds  of  the  quadrant,  and  at  the  bottom  of  each 
page  is  given  the  correction  for  any  number  of  seconds  less  than  ten,  so 
that  the  precision  of  seconds  can  be  obtained  with  almost  the  same  fa- 
cility as  that  of  minutes  with  the  tables  in  common  use.  Moreover, 
near  the  limits  of  the  quadrant,  by  means  of  an  auxiliary  table,<*ines  and 
tangents  are  readily  obtained,  even  for  a  fraction  of  a  second.  The 
method  of  arrangement  of  the  sines  and  tangents  was  suggested  by  a 
table  in  Mackay's  Longitude  ;  but  the  errors  of  that  table,  amounting  to 
several  thousand,  have  been  corrected  by  a  careful  comparison  with  the 
work  of  Ursinus.  By  comparison  with  the  same  standard,  more  than 
two  hundred  errors  (chiefly  in  the  final  figures)  have  been  detected  in 
the  tables  in  common  use. 

The  Table  of  Natural  Sines  and  Tangents  is  of  less  use  than  the  loga- 
rithmic ;  nevertheless,  it  is  often  important  for  reference,  particularly  in 
analytical  geometry  and  the  calculus  ;  and  it  is  useful  as  a  stepping 
stone  to  assist  the  beginner  in  comprehending  the  nature  of  logarithmic 

339660 


REFACE. 


sines  ar.d  tangents.  The  Traverse  Table  commonly  usea  in  this  country 
furnishes  the  latitude  and  departure  to  every  quarter  degree  of  the  quad- 
rant, for  distances  from  1  to  100,  and  occupies  ninety  pages.  The  accom- 
panying table  occupies  but  six  pages,  and  yields  ten  times  greater  pre- 
cision. 

The  Table  of  Meridional  Parts  extends  to  tenths  of  a  mile,  and  grea 
care  has  been  taken  to  insure  its  accuracy.  For  this  purpose,  I  have 
compared  all  the  similar  tables  within  my  reach,  and  among  them  have 
found  two  which  appeared  to  have  been  computed  independently.  Be- 
tween them  there  were  detected  674  discrepancies  in  the  final  figures. 
These  cases  were  all  recomputed,  and  78  errors  were  detected  in  the 
jest  copy  compared.  It  is  probable. that  the  numbers  in  this  table  are 
not  in  every  instance  true  to  the  nearest  tenth  of  a  mile  ;  but  it  is  be 
lieved  that  the  remaining  -errors  are  few  in  number,  as  well  as  minute. 
This  table  is  confidently  pronounced  more  accurate  than  any  similar 
one  with  which  I  have  been  able  to  compare  it. 

The  Table  of  Corrections  to  Middle  Latitude  was  computed  entirely 
anew.  The  corresponding  table  in  common  use,  which  was  originally 
computed  by  Workman,  contains  more  than  four  hundred  errors,  sev- 
eral of  them  amounting  to  two  minutes. 

On  the  whole,  it  is  believed  that  the  accompanying  tables  will  be 
found  more  convenient  to  the  computer  than  any  tables  of  six  decimal 
places  hitherto  published  in  this  country ;  and  that  they  will  be  pro- 
nounced sufficiently  extensive  for  all  purposes  of  academic  and  collegri- 
ite  instruction,  as  well  as  for  practical  mechanics  and  surveyors. 


EXPLANATION  OF  THE  TABLES. 


TABLE  OF  LOGARITHMS  OF  NUMBERS,  pp.  1-20. 

LOGARITHMS  are  numbers  contrived  to  diminish  the  labor  of  Multiplica- 
tion and  Division  by  substituting  in  their  stead  Addition  ancl  Subtrac 
tion.  All  numbers  are  regarded  as  powers  of  some  one  number,  which 
is  called  the  base  of  the  system  ;  and  the  exponent  of  that  power  of  the 
base  which  is  equal  to  a  given  number,  is  called  the  logarithm  of  that 
number. 

The  base  of  the  common  system  of  logarithms  (called,  from  their  in- 
ventor, Briggs'  logarithms)  is  the  number  10.  Hence  all  numbers  are 
to  be  regarded  as  powers  of  10.  Thus,  since 

10°= 1,  0  is  the  logarithm  of  1  in  Briggs'  system  ; 

10'=  10,          1     "  "  10  "  " 

10a=100,        2     "  "  100  "  " 

103=1000,      3     "  "  1000  "  " 

104= 10,000,  4     "  «  10,000 

&c.,  &c.,  &c. ; 

whence  it  appears  that,  in  Briggs'  system,  the  logarithm  of  every  num- 
ber between  1  and  10  is  some  number  between  0  and  1,  i.  e.,  is  a  prop- 
er fraction.  The  logarithm  of  every  number  between  10  and  100  is 
some  number  between  1  and  2,  i.  e.,  is  1  plus  a  fraction.  The  loga- 
rithm of  every  number  between  100  and  1000  is  some  number  between 
2  and  3,  i.  e.,  is  2  plus  a  fraction,  and  so  on. 

The  preceding  principles  may  be  extended  to  fractions  by  means  of 
negative  exponents.  Thus,  since 

10^= 0.1,        — 1  is  the  logarithm  of  0.1          in  Briggs'  system  ; 
10~2=0.01,       —2      "  "          0.01  "  " 

\0~3=0.001,     —3      "  "          0.001 

10~4=0.0001,  —4      "  "          0.0001 

&c.,  &c.,  &c. 

Hence  it  appears  that  the  logarithm  of  every  number  between  1  and 
0.1  is  some  number  between  0  and  — 1,  or  may  be  represented  by  — 1 
plus  a  fraction;  the  logarithm  of  every  number  between  0.1  and  .01  is 
some  number  between  — 1  and  — 2,  or  may  be  represented  by  — 2  plus 


v'\  EXPLANATION    or   THE    TABLES. 

a  fraction  ;  the  logarithm  of  every  number  between  .01  and  .001  is  some 
number  between  — 2  and  — 3,  or  is  equal  to  — 3  plus  a  fraction,  and  so  on. 
The  logarithms  of  most  numbers,  therefore,  consist  of  an  integer  and 
a.  fraction.  The  integral  part  is  called  the  characteristic,  and  may  be 
known  from  the  following 

RULE. 

The  characteristic  of  the  logarithm  of  a  number  greater  than  unity,  is 
cue  less  than  the  number  of  integral  figures  in  the  given  number. 

Thus  the  logarithm  of  297  is  2  plus  a  fraction  ;  that  is,  the  character- 
istic of  the  logarithm  of  297  is  2,  which  is  one  less  than  the  number  of 
integral  figures.  The  characteristic  of  the  logarithm  of  5673.29  is  3 ; 
that  of  73254.1  is  4,  &c. 

The  characteristic  of  the  logarithm  of  a  decimal  fraction  is  a  negative 
number,  and  is  equal  to  the  number  of  places  by  which  its  first  significant 
figure  is  removed  from  the  place  of  units. 

Thus  the  logarithm  of  .0046  is  — 3  plus  a  fraction;  that  is,  the  char- 
acteristic of  the  logarithm  is  — 3,  the  first  significant  figure  4  being 
removed  three  places  from  units. 

The  accompanying  table  contains  the  logarithms  of  all  numbers  from 
I  to  10,000  carried  to  6  decimal  places. 

To  find  the  Logarithm  of  any  Number  between  1  and  100. 

Look  on  the  first  page  of  the  table,  along  the  column  of  numbers  under 
N,  for  the  given  number,  and  against  it,  in  the  next  column,  will  be  found 
the  logarithm,  with  its  characteristic.  Thus, 

opposite  13  is  1.113943,  which  is  the  logarithm  of  13; 
"        65  is  1.812913,  "  "  65. 

To  find  ?//*  Logarith?n  of  any  Number  consisting  of  three  Figures. 

Look  on  one  of  the  pages  from  2  to  20,  along  the  left-hand  column 
marked  N,  for  the  given  number,  and  against  it,  in  the  column  headed  0, 
will  be  found  the  decimal  part  of  its  logarithm.  To  this  the  character- 
istic must  be  prefixed,  according  to  the  rule  already  given.  Thus 

the  logarithm  of  347  will  be  found,  from  page  8,  to  be  2.540329 ; 
"  "     871         "  "  "     18,    "     2.940018. 

As  the  first  two  figures  of  the  decimal  are  the  same  for  several  suc- 
cessive numbers  in  the  table,  they  are  not  repeated  for  each  logarithm 
separately,  but  are  left  to  be  supplied.  Thus  the  decimal  part  of  the 
logarithm  of  339  is  .530200.  The  first  two  figures  of  the  decimal  remain 
the  same  up  to  347 ;  they  are  therefore  omitted  in  the  table,  and  are  to 
be  supplied. 

To  find  the  Logarithm  of  any  Number  consisting  of  four  Figures. 
Find  the  three  left-hand  figures  in  the  column  marked  N  as  before 


EXPLANATION   OP  THE   TABLES.  vii 

«jid  the  fourth  figure  at  the  head  of  one  of  the  other  columns.     Opposite 
to  the  first  three  figures,  and  in  the  column  under  the  fourth  figure,  will 
be  found  four  figures  of  the  logarithm,  to  which  two  figures  from  the 
column  headed  0  are  to  be  prefixed,  as  in  the  former  case.     The  char- 
acteristic, must  be  supplied  by  the  usual  rule.     Thus 
the  logarithm  ©f  3456  is  3.538574 ; 
"     8765  is  3.042752. 

In  sever-ai  df  the  columns  headed  1,  2,  3,  &c.,  small  dots  are  lound  in 
the  place  of  figures.  This  is  to  show  that  the  two  figures  which  are  to 
be  prefixed  from  the  first  column  have  changed,  and  they  are  to  be 
taken  from  the  horizontal  line  directly  below.  The  place  of  the  dots  is 
to  be  supplied  with  ciphers.  Thus 

the  logarithm  of  2045  is  3.310693  ; 
«     9777  is  3.990206. 

The  two  leading  figures  from  the  column  0  must  also  be  taken  from 
the  horizontal  line  below,  if  any  dots  have  been  passed  over  on  the  same 
horizontal  line.  Thus 

the  logarithm  of  1628  is  3.211654. 

To  find  the  Logarithm  of  any  Number  containing  more  than  four 

Figures. 

By  inspecting  the  table,  we  shall  find  that  within  certain  limits  the  log- 
arithms are  nearly  proportional  to  their  corresponding  numbers.     Thus 
the  logarithm  of  7250  is  3.860338  ; 
"  "     7251  is  3.860398  ; 

"  "     7252  is  3.860458  ; 

"  "     7253  is  3.860518. 

Here  the  difference  between  the  successive  logarithms,  called  the 
tabular  difference,  is  constantly  60,  corresponding  to  a  difference  of  unity 
in  the  natural  numbers.  If,  then,  we  suppose  the  logarithms  to  be  pro- 
portional to  their  corresponding  numbers  (as  they  are  nearly^,  a  differ- 
ence of  0.1  in  the  numbers  should  correspond  to  a  difference  of  6  in  the 
logarithms ;  a  difference  of  0.2  in  the  numbers  should  correspond  to  a 
difference  of  12  in  the  logarithms,  &c.  Hence 

the  logarithm  of  7250.1  must  be  3.860344 ; 

"  "     7250.2         "       3.860350; 

"  "     7250.3         "       3.860356; 

&c.,  &c. 

In  order  to  facilitate  the  computation,  the  tabular  difference  is  insert- 
ed on  page  16  in  the  column  headed  D,  and  the  proportional  part  for  the 
fifth  figure  of  the  natural  number  is  given  at  the  bottom  of  the  page. 
Thus,  when  the  tabular  difference  is  60,  the  corrections  for  .1,  .2,  .3 
&c.,  are  seen  to  be  6,  12,  18,  &c. 

If  the  given  number  was  72501,  the  characteristic  of  its  logarithm 
would  be  4,  but  the  decimal  part  would  be  the  same  as  for 


Vlll 


EXPLANATION   OF   THE    TABLES. 


If  it  were  required  to  find  the  correction  for  a  sixth  figure  in  the  nat 
ural  number,  it  is  readily  obtained  from  the  Proportional  Parts  in  the 
table.     Thus,  if  the  correction  for  .5  is  30,  the  correction  for  .05  is  ob 
viously  3. 

As  the  differences  change  rapidly  in  me  first  part  of  the  table,  n 
was  found  inconvenient  to  give  the  proportional  parts  for  each  tabular 
difference ;  accordingly,  for  the  first  seven  pages  they  are  only  given 
for  the  even  differences,  but  the  proportional  parts  for  the  odd  differences 
will  be  readily  found  by  inspection. 
Required  the  logarithm  of  452789. 

The  logarithm  of  452700  is  5.655810 
The  tabular  difference  is  96. 

Accordingly,  the  correction  for  the  fifth  figure,  8,  is  77,  and  for  the 
sixth  figure,  9,  is  8.6,  or  9  nearly.  Adding  these  corrections  to  the  num- 
ber before  found,  we  obtain  5.655896. 

The  preceding  logarithms  do  not  pretend  to  be  perfectly  exact,  bu 
only  the  nearest  numbers  having  but  six  decimal  places.     Accordingly 
when  the  fraction  which  is  omitted  exceeds  half  a  unit  in  the  sixth  deH 
mal  place,  the  last  figure  must  be  increased  by  unity. 
Required  the  logarithm  of  8765432. 

The  logarithm  of  8765000  is  6.942752 

Correction  for  the  fifth  figure  4,  20 

"  "       sixth  figure  3,  1.5 

"  "       seventh  figure  2,  0.1 

Therefore  the  logarithm  of  8765432  is  6.942774. 

Required  the  logarithm  of  234567. 

The  logarithm  of  234500  is  5.370143 

Correction  for  the  fifth  figure  6,  111 

"       sixth  figure  7,  13 

Therefore  the  logarithm  of  234567  is  5.370267. 

To  find  the  Logarithm  of  a  Decimal  Fraction. 

The  decimal  part  of  the  logarithm  of  any  number  is  the  same  as  that 
of  the  number  multiplied  or  divided  by  10,  100,  1000,  &c.  Hence,  for 
a  decimal  fraction,  we  find  the  logarithm  as  if  the  figures  were  integers 
and  prefix  the  characteristic  according  to  the  usual  rule. 

EXAMPLES. 

The  logarithm  of  345.6  is  2.538574 ; 

87.65  is  1.942752; 

"  «          2.345  is  0.370143; 

«  "  .1234  is  1.091315; 

«  «    •        005678  is  3.754195. 


EXPLANATION    OF    THE    TABLC 3.  .x 

The  minus  sign  is  placed  over  the  characteristic  to  show  that  this 
alone  is  negative,  while  the  decimal  part  of  the  logarithm  is  positive. 

To  find  the  Logarithm  of  a  Vulgar  Fraction. 

We  may  reduce  the  vulgar  fraction  to  a  decimal,  and  find  its  loga- 
rithm by  the  preceding  rule  ;  or,  since  the  value  of  a  fraction  is  equal  to 
the  quotient  of  the  numerator  divided  by  the  denominator,  we  may  sub- 
tract the  logarithm  of  the  denominator  from  that  of  the  numerator ;  the 
difference  will  be  the  logarithm  of  the  quotient. 
Required  the  logarithm  of  T3g-,  or  0.1875. 

From  the  logarithm  of  3,        .0.477121, 
Subtract  the  logarithm  of  16,  1.204120. 
Leaves  logarithm  of  T\,  or  .1875,  1.273001. 

Tn  the  same  manner  we  find 

the  logarithm  of  ^  is  2.861697 ; 
"     }ff  is  1.147401. 

To  find  the  natural  Number  corresponding  to  any  Logarithm. 

Look  in  the  table  in  the  column  headed  0  for  the  first  two  figures  of 
the  logarithm,  neglecting  the  characteristic ;  the  other  four  figures  are 
to  be  looked  for  in  the  same  column,  or  in  one  of  the  nine  following  col- 
umns ;  and  if  they  are  exactly  found,  the  first  three  figures  of  the  corre- 
sponding number  will  be  found  opposite  to  them  in  the  column  headed 
N,  and  the  fourth  figure  will  be  found  at  the  top  of  the  page.  This  num- 
ber must  be  made  to  correspond  with  the  characteristic  of  the  given 
logarithm  by  pointing  off  decimals  or  annexing  ciphers.  Thus 

the  natural  number  belonging  to  the  logarithm  4.370143  is  23450  ; 

1.538574  is  34.56. 

If  the  decimal  part  of  the  logarithm  can  not  be  exactly  found  in  the 
table,  look  for  the  nearest  less  logarithm,  and  take  out  the  four  figures 
of  the  corresponding  natural  number  as  before ;  the  additional  figures 
may  be  obtained  by  means  of  the  Proportional  Parts  at  the  bottom  of 
the  page. 

Required  the  number  belonging  to  the  logarithm  4.368399. 

On  page  6,  we  find  the  next  less  logarithm  .368287. 

The  four  corresponding  figures  of  the  natural  number  are  2335. 
Their  logarithm  is  less  than  the  one  proposed  by  112.  The  tabular 
difference  is  186 ;  and,  by  referring  to  the  bpttom  of  page  6,  we  find 
that,  with  a  difference  of  186,  the  figure  corresponding  to  the  Propor- 
tional Part  112  is  6.  Hence  the  five,  figures  of  the  natural  number  are 
23356 ;  and,  since  the  characteristic  of  the  proposed  logarithm  is  4,  these 
five  figures  are  all  integral. 

Required  the  number  belonging  to  logarithm  5.345678. 

The  next  less  logarithm  in  the  table  is  .345570 

Their  difference  7's  108. 


x  EXPLANATION   OF   THE   TABLES. 

The  first  four  figures  of  the  natural  number  are  2216. 

With  the  tabular  difference  196,  the  fifth  figure  corresponding  to  108 
>a  seen  to  be  5.  with  a  remainder  of  10.  which  furnishes  a  sixth  figure  5 
nearly.  Hence  the  required  number  is  221' 

In  the  same  manner  we  find 

the  number  corresponding  to  logarithm  3  ~  $  ; 


*  «  T.IV17S17  is  .444444. 

TABLE  OF  NATURAL  SIN  TANGENTS,  pp.  116-133. 

This  is  a  table  of  natural  sines  and  tangents  for  every  degree  ana 
minute  of  the  quadrant,  carried  to  six  places  of  figures.  Since  the  ra- 
dius of  the  circle  is  supposed  to  be  unity,  t: 

less  than  unity.  These  sines  are  expressed  in  decimal  parts  of  the 
radius  ;  and.  although  the  decimal  point  is  not  written  in  the  table,  it 
must  always  be  prefixed.  The  degrees  are  arranged  in  order  at  the  top 
of  the  page,  and  the  minutes  in  the  left  hand  vertical  column.  Directly 
under  the  given  number  of  -  at  the  top  of  the  1  opposite 

to  the  minutes  on  the  left,  will  be  found  the  sine  required.     The  tw--> 
leading  figures  are  repeated  at  intervals  of  ten  minutes.     Thus 
the  sine  of  s.  11  2330: 

" 

The  same  number  in  the  table  is  both  the  sine  of  an  arc  and  t! 
sine  of  its  complement.     The  degrees  for  the  cosines  must  be  sought  at 
the  bottom  of  the  page,  and  the  minutes  on  the  right.     Thus 

the  cosine  oioJ    2:»  •  .4631 

..  „ 

If  a  sine  is  required  for  an  arc  consisting  of  degrees,  minuies.  and  sec 
ondsj  it  may  be  found  by  means  of  the  line  at  the  bottom  of  each  page. 
which  gives  the  proportional  part  corresponding  to  one  second  of  arc 
Required  the  sine  of  8°  9'  10". 

The  sine  of  8°  9'  is  .141: 

By  referring  to  the  bottom  of  page  116,  in  the  column  mui 
find  the  correction  for  1"  is  4.80  ;  hence  the  correction  for  10"  must  be 
48,  which,  added  to  the  number  above  found,  gives  for  the  sine  of  Sc 
9'  10",  .141813. 

In  the  same  manner  we  find 

the  cosine  of  56°  34'  28"  is  .550S53. 

It  will  be  observed,  that  since  the  cosines  decrease  while  the  arcs  m 
crease,  the  correction  for  the  2S  '  is  to  be  subtracted  from  the  cosine 

34. 

The  arrangement  of  the  table  of  natural  tangents  is  similar  to  that  of 

the  table  of  sines.     The  tangents  for  arcs  less  than  45°  are  all  less  than 

radius,  and,  consist  wholly  of  decimals.     For  arcs  above  45C.  the  tan- 

are  all  greater  than  radius  and  contain  both  integral  and  decimal 


EXPLANATION    OF   THE   T  A  111.1:9.  xj 

ngures.     The  proportional  parts  at  the  bottom  of  each  page  enable  us 
readily  to  find  the  correction  for  seconds.     Thus 

the  natural  tangent  of  32°  29'  18"  is  .636784  ; 
"      74°  35'  55"  is  3.63014. 

To  find  the  Number  of  Degrees,  Minutes,  and  Seconds  belonging  to  « 
given  Sine  or  Tangent. 

If  the  given  sine  or  tangent  is  found  exactly  in  the  table,  the  corre- 
sponding degrees  will  be  found  afc  the  top  of  the  page,  and  the  minutes 
on  the  left  hand.  But  when  the  given  number  is  not  found  exactly  in 
the  table,  look  for  the  sine  or  tangent  which  is  next  less  than  the  pro- 
posed one,  and  take  out  the  corresponding  degrees  and  minutes.  Find, 
also,  the  difference  between  this  tabular  number  and  the  number  pro- 
posed, and  divide  it  by  the  proportional  part  for  1"  found  at  the  bottom 
of  the  page ;  the  quotient  will  be  the  required  number  of  seconds. 

Required  the  arc  whose  sine  is  .750000. 

The  next  less  sine  in  the  table  is  .749919,  the  arc  corresponding  to 
which  is  48°  35'.  The  difference  between  this  sine  and  that  proposed 
is  81,  which,  divided  by  3.21,  gives  25.  Hence  the  required  arc  is  48° 
35'  25". 

In  the  same  manner  we  find 

the  arc  whose  tangent  is  2.000000,  to  be  63°  26'  6". 

TABLE  OP  NATURAL  SECANTS,  pp.  134-5. 

This  is  a  table  of  natural  secants  for  every  ten  minutes  of  the  quad- 
rant carried  to  seven  places  of  figures.  The  degrees  are  arranged  in 
order  in  the  first  vertical  column  on  the  left,  and  the  minutes  at  the  top 
of  the  page.  Thus 

the  secant  of  21°  20'  is  1.073561 ; 
"  "    81°  50'  is  7.039622. 

If  a  secant  is  required  for  a  number  of  minutes  not  given  in  the  table, 
the  correction  for  the  odd  minutes  may  be  found  by  means  of  the  last 
vertical  column  on  the  right,  which  shows  the  proportional  part  for  one 
minute. 

Let  it  be  required  to  find  the  secant  of  30°  33'. 

The  secant  of  30°  30'  is  1.160592. 

The  correction  for  1'  is  198.9,  which,  multiplied  by  3,  gives  597 
Adding  this  to  the  number  before  found,  we  obtain  1.161189. 

For  a  cosecant,  the  degrees  must  be  sought  in  the  right-hand  vertical 
column,  and  the  minutes  at  the  bottom  of  the  page.     Thus 
the  cosecant  of  47°  40'  is  1.352742. 

TABLE  OF  LOGARITHMIC  SINES  AND  TANGENTS,  pp.  21-115. 

This  is  a  table  of  the  logarithms  of  the  sines  and  tangents  for  every 
ten  seconds  of  the  quadrant,  carried  to  six  places  of  decimals  The  de- 


in  EXPLANATION    OF    THE    TABLES. 

grees  and  seconds  are  placed  at  the  top  of  the  page,  and  the  minutes  .n 
the  left  vertical  column.  After  the  first  two  degrees,  the  three  leading 
figures  in  the  table  of  sines  are  only  given  in  the  column  headed  0",  and 
are  to  be  prefixed  to  the  numbers  in  the  other  columns,  as  in  the  table 
of  logarithms  of  numbers.  Also,  where  the  leading  figures  change,  this 
change  is  indicated  by  dots,  as  in  the  former  table.  The  correction  foi 
any  number  of  seconds  less  than  10  is  given  at  the  bottom  of  the  page. 

To  find  the  Logarithmic  Sine  or  Tangent  of  a  given  Arc. 

Look  for  the  degrees  at  the  top  of  the  page,  the  minutes  on  the  lelt 
hand,  and  the  next  less  tenth  second  at  the  top ;  then,  under  the  seconds, 
and 'opposite  to  the  minutes,  will  be  found  four  figures,  to  which  the 
three  leading  figures  are  to  be  prefixed  from  the  column  headed  0" ;  to 
this  add  the  proportional  part  for  the  odd  seconds  from  the  bottom  of 
the  page. 

Required  the  logarithmic  she  of  24°  27'  34". 

The  logarithmic  sine  of  24°  27'  30"  is  9.617033. 
Proportional  part  for  4"  is  18. 

Logarithmic  sine  of  24°  27'  34"  is       9.617051. 

This  is  the  logarithm  of  .414049  found  in  the  table  of  natural  sines  on 
page  120.  The  natural  sine  being  less  than  unity,  the  characteristic 
of  its  logarithm  is  negative.  Tc  obviate  this  inconvenience,  the  char- 
acteristics in  the  table  nave  all  been  increased  by  10 ;  or  the  logarith- 
mic sines  may  be  regarded  as  the  logarithms  of  natural  sines  computed 
for  a  radius  of  10,000,000,000. 

Required  the  logarithmic  tangent  of  73°  35'  43". 

The  logarithmic  tangent  of  73°  35'  40"  is  10.531031. 
Proportional  part  for  3"  is  23. 

Logarithmic  tangent  of  73°  35'  43"  10.531054. 

When  a  cosine  is  required,  the  degrees  and  seconds  must  be  sought 
at  the  bottom  of  the  page,  and  the  minutes  on  the  right,  and  the  correc 
tion  for  the  odd  seconds  must  be  subtracted  from  the  number  in  the  table 
Required  the  logarithmic  cosine  of  59°  33'  47". 

The  logarithmic  cosine  of  59°  33'  40"  i-s  9.704682. 
Proportional  part  for  7"  is  25. 

Logarithmic  cosine  of  59°  33'  47"  is  9.704657. 
So,  also,  the  logarithmic  cotangent  of  37°  27'  14"  is  found  to  be  10.115744. 
The  proportional  parts  given  at  the  bottom  of  each  page  correspond 
to  the  degrees  at  the  top  oi  the  page  increased  by  30',  and  are  not 
strictly  applicable  to  any  other  number  of  minutes ;  nevertheless,  the 
differences  of  the  sines  change  so  slowly,  except  near  the  commence- 
ment of  the  quadrant,  that  the  error  resulting  from  using  these  numbers' 
for  every  part  of  the  page  will  sa  Jom  exceed  a  unit  in  the  sixth  deci- 
mal place.  For  the  first  two  degrees,  the  differences  change  so  rapidly 


EXPLANATION    OF   THE   TABLES.  xii 

tuat  the  proportional  part  for  1"  is  given  for  each  minute  in  the  right- 
hand  column  of  the  page.  The  correction  for  any  number  of  seconds 
less  than  ten  will  be  found  by  multiplying  the  proportional  part  for  i" 
by  the  given  number  of  seconds. 

Required  the  logarithmic  sine  of  1°  17'  33". 

The  logarithmic  sine  of  1°  17'  30"  is  8.352991 

The  correction  for  3"  is  found  by  multiplying  93.4  by  3,  which  gives 
280.     Adding  this  to  the  above  tabular  number,  we  obtain 
the  sine  of  1°  IT  33",  8.353271. 

A  similar  method  may  be  employed  for  several  of  the  first  degrees 
of  the  quadrant,  if  the  proportional  parts  at  the  bottom  of  the  page  are 
not  thought  sufficiently  precise.  This  correction  may,  however,  be  ob- 
tained pretty  nearly  by  inspect:on  from  comparing  the  proportional 
parts  for  two  successive  degrees.  Thus,  on  page  26,  the  correction  for 
1",  corresponding  to  the  sine  of  2°  30',  is  48  ;  the  correction  for  1",  cor- 
responding to  the  sine  of  3°  30',  is  34.  Hence  the  correction  for  1", 
corresponding  to  the  sine  of  3°  0',  must  be  about  41  ;  and  in  the  same 
manner  we  may  proceed  for  any  other  part  of  the  table. 

Near  the  close  of  the  quadrant,  the  tangents  vary  so  rapidly,  that  the 
same  arrangement  of  the  table  is  adopted  as  for  the  commencement  of 
the  quadrant.  For  the  last  as  well  as  the  first  two  degrees  of  the  quad- 
rant, the  proportional  part  to  1"  is  given  for  each  minute  separately. 
These  proportional  parts  are  computed  for  the  minutes  placed  opposite 
to  them,  increased  by  30' ,  and  are  not  strictly  applicable  to  any  other 
number  of  seconds  ;  nevertheless,  the  differences  for  the  most  part 
change  so  slowly,  that  the  error  resulting  from. using  these  numbers  for 
every  part  of  the  same  horizontal  line  is  quite  small.  When  great  ac- 
curacy is  required,  the  table  on  page  114  may  be  employed  for  arcs 
near  the  limits  of  the  quadrant.  This  table  furnishes  the  differences  be- 
tween the  logarithmic  sines  and  the  logarithms  of  the  arcs  expressed  in 
seconds.  Thus 

the  logarithmic  sine  of  0°  5'  is  7.162696 ; 
the  logarithm  of  300"  (=5;)  is  2.477121  ; 

the  difference  is  4.685575. 

This  is  the  number  found  on  page  114,  under  the  heading  log.  sine 
A — log.  A",  opposite  5  min. ;  and  in  a  similar  manner  the  other  numbers 
in  the  same  column  are  obtained.  These  numbers  vary  quite  slowly 
for  two  degrees  ;  and  hence,  to  find  the  logarithmic  sine  of  an  arc  less 
than  two  degrees,  we  have  but  to  add  the  logarithm  of  the  arc  expressed 
iu  seconds  to  the  appropriate  number  found  in  this  table. 
Required  the  logarithmic  sine  of  0°  7'  22". 

Tabular  number  from  page  114,  4.685575. 
The  logarithm  of  442"  is  2.645422. 

Logarithmic  sine  of  0°  T  22"  is  7.330997 


xiv  EXPLANATION    OF   THE    TABLES. 

The  logarithmic  tangent  of  an  arc  less  than  two  degrees  is  found  in 
a  similar  manner. 
Required  the  logarithmic  tangent  of  0°  27'  36". 

Tabular  number  from  page  114,       4.685584. 

The  logarithm  of  1656"  is  3.219060. 

Logarithmic  tangent  of  0°  27'  36"  is  7.904644. 

The  column  headed  log.  cot.  A+log.  A"  is  found  by  adding  -the  log- 
arithmic cotangent  to  the  logarithm  of  the  arc  expressed  in  seconds. 
Hence,  to  find  the  logarithmic  cotangent  of  an  arc  less  than  two  degrees, 
we  must  subtract  from  the  tabular  number  the  logarithm  of  the  arc  in 
seconds. 

Required  the  logarithmic  cotangent  of  0°  27'  36". 

Tabular  number  from  page  114,  15.314416. 

The  logarithm  of  1656"  is  3.219060. 

Logarithmic  cotangent  of  0°  27'  36"  is  12.095356. 
The  same  method  will,  of  course,  furnish  cosines  and  cotangents  ol 
arcs  near  90°. 

The  secants  and  cosecants  are  omitted  in  this  table,  since  they  are 
easily  derived  from  the  cosines  and  sines. 

The  logarithmic  secant  is  found  by  subtracting  the  logarithmic  cosine 
from  20  ;  and  the  logarithmic  cosecant  is  found  by  subtracting  the  loga- 
rithmic sine  from  20. 

Thus  we  have  found  the  logarithmic  sine  of  24°  27'  34"  to  be  9.617051. 
Hence  the  logarithmic  cosecant  of  24°  27'  34"  is  10.382949. 

The  logarithmic  "cosine  of  54°  12'  40"  is  9.767008. 

Hence  the  logarithmic  secant  of  54°  12'  40"  is  10.232992. 

To  find  the  Arc  corresponding  to  a  given  Logarithmic  Sine  or  Tangent 

If  the  given  number  is  found  exactly  in  the  table  the  corresponding 
degrees  and  seconds  will  be  found  at  the  top  of  the  page,  and  the  min- 
utes on  the  left.  But  when  the  given  number  is  not  found  exactly  in 
the  table,  look  for  the  sine  or  tangent  which  is  next  less  than  the  pro- 
posed one,  and  take  out  the  corresponding  degrees,  minutes,  and  sec- 
onds. Find,  also,  the  difference  between  this  tabular  number  and  the 
number  proposed,  and,  corresponding  to  this  difference,  at  the  bottom  of 
the  page  will  be  found  a  certain  number  of  seconds,  which  is  to  be  added 
vO  the  arc  before  found. 

Required  the  arc  corresponding  to  the  logarithmic  sine  9.750000. 

The  next  less  sine  in  the  table  is  9.749987. 

The  arc  corresponding  to  which  is  34°  13'  0". 

The  difference  between  its  sine  and  the  one  proposed  is  13,  corre- 
sponding to  which,  at  the  bottom  of  the  page,  we  find  4"  nearly.  Hence 
the  required  arc  is  34°  19'  4-". 


EXPLANATION  OF  THE  TABLES,          xv 

In  the  same  manner  we  find  the  arc  corresponding  to  logarithmic  tan 
gent  10.250000,  to  be  60°  38'  57". 

When  the  arc  falls  within  the  first  two  degrees  of  the  quadrant,  the 
odd  seconds  may  be  found  by  dividing  the  difference  between  the  tab- 
ular number  and  the  one  proposed,  by  the  proportional  part  for  1".  We 
thus  find  the  arc  corresponding  to  logarithmic  sine  8.400000,  to  be  1° 
26'  22"  nearly. 

We  may  employ  the  same  method  for  the  last  two  degrees  of  the 
quadrant  when  a  tangent  is  given ;  but  near  the  limits  of  the  quadrant 
it  is  better  to  employ  the  auxiliary  table  on  page  114.  If  we  subtract 
the  corresponding  tabular  number  on  page  114  from  the  given  logarith- 
mic sine,  the  remainder  will  be  the  logarithm  of  the  arc  expressed  in 
seconds. 

Required  the  arc  corresponding  to  logarithmic  sine  7.000000. 

We  see,  from  page  22,  that  the  arc  must  be  nearly  3' ;  the  correspond 
ing  tabular  number  on  page  114  is  4.685575. 

The  difference  is  2.314425; 
which  is  the  logarithm  of  206."265. 

Hence  the  required  arc  is  3'  26."265. 

In  the  same  manner  we  find  the  arc  corresponding  to  logarithmic 
tangent  8.184008,  to  be  0°  52'  35/;. 

TABLE  FOR  THE  LENGTHS  OF  CIRCULAR  ARCS,  p.  135. 

This  table  contains  the  lengths  of  every  single  degree  up  to  60,  and 
at  intervals  often  degrees  up  to  180  ;  also  for  every  minute  and  second 
up  to  20.  The  lengths  are  all  expressed  in  decimal  parts  of  radius. 

Required  the  length  of  an  arc  of  57°  17'  44."8. 

Take  out  from  their  respective  columns  the  lengths  answering  to  each 
of  these  numbers  singly,  and  add  them  all  together  thus : 

57° 0.9948377 

17' 0049451 

40" 0001939 

4" 0000194 

0."8  .  .0000039 


The  sum  is         1.0000000. 

That  is,  the  length  of  an  arc  of  57°  17'  44."8  is  equal  to  the  radius  of 
the  circle. 

TRAVERSE  TABLE,  pp.  136-141. 

This  table  shows  the  difference  of  latitude  and  the  departure  to  four 
decimal  places  for  distances  from  1  to  10,  and  for  bearings  from  0°  to 
90°rat  intervals  of  15'.     If  the  bearing  is  less  than  45°,  the  angle  will 
be  found  on  the  left  margin  of  one  of  the  pages  of  the  table,  and  the  dis 
*ance  at  the  top  or  bottom  of  the  page  ;  the  difference  of  latitude  wil 


A  t  i  EXPLANATION    OF    THE    TABLES 

be  found  in  the  column  headed  lat.  at  the  top  -of  the  page,  and  the  de 
parture  in  the  column  headed  dep.  If  the  bearing  is  more  than  45°,  the 
angle  will  be  found  on  the  right  margin,  and  the  difference  of  latitude 
will  be  found  in  the  column  marked  lat.  at  the  bottom  of  the  page,  and 
the  departure  in  the  other  column.  The  latitudes  and  departures  for 
different  distances  with  the  same  bearing,  are  proportional  to  the  dis- 
tances. Therefore  the  distances  may  be  reckoned  as  tens,  hundreds,  or 
thousands,  if  the  place  of  the  decimal  point  in  each  departure  and  differ- 
ence of  latitude  be  changed  accordingly. 

Required  the  latitude  and  departure  for  the  distance  32.25,  and  the 
bearing  10°  30'. 

On  page  136,  opposite  to  10°  30',  we  find  the  following  latitudes  and 
departures,  proper  attention  being  paid  to  the  position  of  the  decimal 
-joints. 

Distance.  Diff.  Lat.  Dep. 

30  29.498  5.467 

2  1.966  .364 

.2  .197  .036 

.05  .049  .009 


32.25  31.710  5.876. 

TABLE  OF  MERIDIONAL  PARTS,  pp.  142-148. 

This  table  gives  the  length  of  the  enlarged  meridian  on  Mercators 
Chart  to  every  minute  of  latitude  expressed  in  geographical  miles  and 
tenths  of  a  mile.  The  degrees  of  latitude  are  arranged  in  order  at  the 
top  of  the  page,  and  the  minutes  en  both  the  right  and  left  margins. 
Under  the  degrees  and  opposite  to  the  minutes  are  placed  the  merid- 
ional parts  corresponding  to  any  latitude  less  than  80°.  Thus 
the  meridional  parts  for  latitude  12°  23'  are  748.9 ; 

57°  42'  are  4260.5. 

TABLE  OF  CORRECTIONS  TO  MIDDLE  LATITUDE,  p.  149. 

This  table  is  used  in  Navigation  for  correcting  the  middle  latitude 
The  given  middle  latitude  is  to  be  found  either  in  the  first  or  last  verti- 
cal column,  opposite  to  which,  and  under  the  given  difference  of  latitude, 
is  inserted  the  proper  correction  in  minutes,  to  be  added  to  the  middle 
latitude  to  obtain  the  latitude  in  which  the  meridian  distance  is  accu 
rately  equal  to  the  departure.  Thus,  if  the  middle  latitude  is  41°,  and 
the  difference  of  latitude  14°,  the  correction  will  be  found  to  be  25', 
which,  added  to  the  middle  latitude,  gives  the  corrected  middle  latitude 
41°  25'. 


A  TABLE 

* 

OP 

LOGARITHMS  OF  lUMBEHS 

FROM    1    TO    10,000. 

N. 

Log. 

K. 

Log. 

N. 

Log. 

N. 

Log. 

i 

o.oooooo 

26 

.4i4973 

5i 

.707570 

76 

.880814 

52 

o.3oio3o 

27 

.43i364 

52 

.716003 

77 

.886491 

3 

0.477121 

28 

.447i58 

53 

.724276 

78 

.892095 

'4 

0.602060 

29 

.462398 

54 

.732394 

79 

.897627 

5 

0.698970 

3o 

.477121 

55 

•74o363 

80 

.903090 

6 

0.778151 

3i 

.491362 

56 

.748188 

8  1 

.908485 

7 

0.845098 

32 

.5o5i5o 

57 

.755875 

82 

.913814 

8 

0.903090 

33 

.5i85i4 

58 

.763428 

83 

.919078 

9 

0.954243 

34 

.53i479 

59 

.770852 

84 

.924279 

10 

i  .000000 

35 

.544o68 

60 

.778151 

85 

.929419 

ii 

.041393 

36 

.5563o3 

61 

.78533o 

86 

.934498 

12 

.079181 

37 

.568202 

62 

.792392 

87 

.939519 

i3 

.113943 

38 

.579784 

63 

.799341 

88 

.  944483 

i4 

.146128 

39 

.591065 

64 

.806180 

89 

.949390 

i5 

.176091 

4o 

.602060 

65 

.812913 

9° 

.954243 

16 

.204120 

4i 

.612784 

66 

.819544 

91 

.959041 

J7 

.23o449 

4a 

.623249 

67 

.826075 

92 

.963788 

18 

.255273 

43 

.633468 

68 

.832509 

93 

.968483 

19 

.278754 

44 

.643453 

69 

.838849 

94 

.973128 

2Q 

.3ojo3o 

45 

.653213 

70 

.845098 

95 

.977724 

21 

.322219 

46 

.662758 

71 

.85i258 

96 

.982271 

22 

.342423 

47 

.672098 

72 

.857332 

97 

.986772 

23 

.361728 

48 

.681241 

73 

.863323 

98 

.991226 

24 

.380211 

49 

.690196 

74 

.869232 

99 

.995635 

25 

.397940 

5o 

.698970 

75 

.875o6i 

100 

2.OOOOOO 

N.B.  In  the  following  table,  the  two  leading  figures  in  the  first  column 

of  logarithms  are  to  be  prefixed  to  all  the  numbexs  of  the  same  horizontal 

line  in  the  next  nine  columns  ;  but  when  a  point  (.)  occurs,  its  place  is  to 

be  suppHfed  by  a  cipher,  and  the  two  leading  figures  are  to  be  taken  from 

the  next  lower  line. 

LOGARITHMS    OF    NUMBERS. 


Nj   0.    1  ,- 

2  • 

3 

.4     5 

6 

7 

8 

9 

D. 

100 

oooooo  o434 

0868 

i3oi  i  1734 

2166 

2598 

3o29 

346i 

389i 

432 

IOI 

4321  475i 

5x8i 

56o9  6o38 

6466 

6894 

7321 

7748 

8174 

428 

IO2 

8600  9026 

945i 

9876  .3oo 

.724 

ii4? 

1670 

i993 

24i5 

424 

io3 

012837  3269 

368o 

4ioo  452i 

49&>  53Co 

5779 

6i97 

6616 

419 

io4 

7o33  745i 

•7868 

8284  8700 

9116 

9532 

9947 

.36i 

.775 

4x6 

io5 

021189  i6o3 

2016 

2428  2841 

3252 

3664 

4o75 

4486 

4896 

419 

1  06 

53o6  57i5 

6i25 

6533  6942 

735o 

7757 

8i64 

857i 

8978 

4o8 

107 

9384  9789 

.i95 

.600  ioo4 

i4o8 

1812 

2216 

26i9 

3021 

4o4 

108 

o33424  |  3826 

4227 

4628  $029 

543o 

583o 

623o 

6629 

7028 

4oo 

io9 

7426  7825 

8223 

8620  9017 

94i4 

9811 

.207 

.602 

.998 

396 

no 

041393  I 

i787 

2l82 

2676  2969 

3362 

3755 

4i48 

454o 

4932 

393 

III 

5323 

57i4 

6io5 

6495  6885 

7275 

7664 

8o53 

8442 

883o 

389 

112 

9218 

96o6 

9993 

.38o  .766 

ii53 

i538 

1924 

23o9 

2694 

386 

n3 

053078 

3463 

3846 

423o.  46i3 

4996 

5378 

6760 

6142 

6524 

382 

n4 

6905 

7286 

7666 

8o46%  8426 

88o5 

9i85 

9563 

9942 

.320 

379 

n5 

060698 

io75 

i452 

1829  2206 

-2582 

2958 

3333 

37o9 

4o83 

376 

116 

4458 

4832 

5206 

558o  5953 

6326 

6699 

7071 

7443 

7815 

373 

117 

8186 

8557 

8928 

9298  9668 

..38 

•  4o7 

.776 

ii45 

i5i4 

369 

118 

071882 

2250 

261-7 

2986  3352 

3718 

4o85 

445  1 

48i6 

5i83 

366 

ii9 

5547 

59I2 

6276 

664o  7004 

736~8 

773i 

8094 

8457 

8819 

363 

120 

9181 

9543 

9904 

.266  ;  .625 

.987 

1  34? 

1707 

2067 

2426 

36o 

121 

082785 

3i44 

35o3 

386i  4219 

4576 

4934 

6291 

5647  6o°4 

357 

N. 

0 

1 

2 

3 

4   ||  5 

6 

7    8 

9 

D. 

434 

43 

87 

i3o 

1  74 

217 

260 

3o4 

34? 

39i 

432 

43 

86 

i3o 

I73 

216 

269 

302 

346 

389 

43o 

43 

86 

129 

I72 

2l5 

258 

3oi 

344 

387 

428 

43 

86 

128 

I7I 

2l4 

257 

3oo 

342 

385 

426 

43 

85 

128 

I70 

213 

256 

298 

34i 

383 

424 

42 

85 

127 

I70 

212 

254 

297 

33o 

382 

422 

42 

84 

127 

169 

211 

253 

295 

338 

38o 

420 

42 

84 

126 

168 

210 

252 

294 

336 

378 

4x8 

42 

84 

125 

167 

209 

25l 

293 

334 

376 

! 

4i6 

42 

83 

125 

1  66 

208 

25o 

291 

333 

3?4 

4x4 

4i 

83 

124 

166 

207 

248 

290 

33i 

373 

412 

4i 

82 

124 

i65 

206 

247 

288 

33o 

37i 

4io 

4i 

82 

123 

1  64 

2O5 

246 

287 

328 

369 

4o8 

4i 

82 

122 

i63 

204 

245 

286 

326 

367 

4o6 

4i 

81 

122 

162 

203 

.  244 

284 

325 

365 

4o4  « 

4o 

Bi 

121 

162 

2O2 

242 

283 

323 

364 

402  £a 

4o 

80 

121 

161 

201 

241 

281 

322 

362 

(D 

4oo  ^ 

4o 

80 

120 

160 

200 

240 

280 

320 

36o 

a 

398  1 

4o 

80 

II9 

i5o 

199 

239 

279 

3i8 

358 

£  • 

J 

396  o 

4o 

79 

II9 

i58 

I98 

238 

277 

3i7 

356 

ID 

5 

W  ! 

39 

79 

118 

1  58 

I97 

236 

276 

3i5 

355 

H-i 

392  o 

39 

78 

118 

i57 

I96 

235 

274 

3x4 

353 

39o  CU 

39 

78 

xi7 

i56 

i95 

234 

273 

3l2 

35i 

388 

39 

78 

116 

i55 

194 

233 

272 

3io 

349 

386 

39 

77 

116 

1  54 

i93 

232 

270 

3o9 

34? 

384 

38 

77 

ii5 

1  54 

192 

230 

269 

307 

346 

382 

38 

76 

iilS 

i53 

191 

229 

267 

3o6 

344 

38o 

38 

76 

n4 

152 

190 

228 

266 

3o4 

342 

378 

38 

76 

Ii3 

i5i 

189 

227 

265 

302 

34o 

376 

38 

75 

li3 

i5o 

1  88 

226 

263 

3oi 

338 

374 

37 

75 

112 

i5o 

187 

224 

262 

299 

337 

372 

37 

74 

112 

1  49 

186 

223 

260 

298 

335 

37o 
368 

37 
37 

74 

74 

III 

no 

i48 
147 

i85 
1  84 

222 

221 

258 

296 
294 

333 
t3i 

366 

37 

73 

IIO 

i46 

i83 

220 

256 

293 

329 

364 

36 

73 

109 

i46 

182 

218 

255 

291 

3a8 

362 

36 

72 

109 

i45 

181 

217 

253 

290 

326 

36o 

36 

72 

108 

i44 

180 

216 

•Si 

288 

324 

LOGARITHMS    OF    NUMBERS. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

122 

o8636o 

6716 

7071 

7426 

7781 

8i36 

8490 

8845 

9198 

9662  355 

123 

9906 

.268 

.611 

.963 

i3i5 

1667 

2018 

2370 

272I 

3071 

35i 

124 

098422 

3772 

4l22 

447i 

4820 

6169 

55i8 

-5866 

62l5 

6662 

349 

125 

6910 

7267 

7604 

795i 

8298 

8644 

8990 

9335 

9681 

..26 

346 

126 

100371 

0716 

1069 

i4o3 

1747 

2091 

2434 

2777 

3lI9 

3462 

343 

127 

38o4 

4i46 

4487 

4828 

6169 

55io 

585i 

6191 

653i 

6871 

34i 

128 

7210 

7649 

7888 

8227 

8565 

8903 

9241 

9679 

9916 

.253 

338 

129 

110690 

0926 

1263 

1699 

1934 

2270 

2606 

2940 

3275 

3609 

335 

i3o 

3943 

4277 

46u 

4944 

6278 

56u 

5943 

6276 

6608 

6g4o 

333 

i3i 

-7271 

7603 

7934 

8266 

8696 

8926 

9266 

9686 

9916 

.245 

33o 

132 

120674 

0903 

I23l 

1660 

1888 

2216 

2544 

2871 

3198 

3525 

328 

i33 

3852 

4178 

45o4 

483o 

5i56 

548i 

58o6 

6i3i 

6456 

6781 

325 

1  34 

7106 

7429 

7753 

8076- 

8399 

8722 

9o45 

9368 

9690 

.  .  12 

323 

i35 

i3o334 

o655 

0977 

1298 

1619 

I939 

2260 

2680 

2900 

3219 

321 

i36 

3539 

3858 

4177 

4496 

48i4 

5i3§ 

545i 

6769 

6086 

64o3 

3i8 

i37 

6721 

7o37 

7354 

7671 

7987 

83o3 

8618 

8934 

9249 

9564 

3x5 

i38 

9879 

.194 

.5o8 

.822 

n36 

i45o 

i763 

2076 

2389 

2702 

3:4 

i39 

i43oi5 

3327 

3639 

3961 

4263 

4574 

4885 

6196 

55o7 

58i8 

3n 

i4o 

6128 

6438 

6748 

7068 

7367 

7676 

7986 

8294 

86o3 

8911 

309 

i4i 

9219 

9627 

9835 

.142 

.449 

.766 

io63 

1370 

i676 

1982 

3o7 

142 

162288 

2594 

2900 

3206 

35io 

38i5 

4l20 

4424 

4728 

5o32 

3o5 

i43 

5336 

564o 

5943 

6246 

6549 

6862 

7i54 

7457 

7769 

8061 

3o3 

i44 

8362 

8664 

8966 

9266 

9667 

9868 

.168 

•  469 

.769 

1068 

3oi 

i45 

i6i368 

1667 

1967 

2266 

2664 

2863 

3i6i 

346o 

3758 

4o55 

299 

i46 

4353 

465o 

4947 

5244 

554i 

5838 

6i34 

643o 

6726 

7022 

297 

147 

73i7 

76  1  3 

7908 

8ao3 

8497 

8792 

9086 

9380 

9674 

9968 

296 

1  48 

170262 

o555 

o848 

n4i 

i434 

1726 

2019 

23ll 

26o3 

2896 

293 

N.    0 

1 

2  |  3 

4  ||  5 

6 

7 

8 

9 

TT" 

358 

36 

72 

.107 

i43 

179 

2l5 

261 

286 

322 

356 

36 

71 

107 

i4a 

178 

9X4 

249 

286 

320 

354 

35 

71 

1  06 

142 

177 

212 

248 

283 

319 

352 

35 

7° 

1  06 

i4i 

176 

211 

246 

282 

3i7 

35o  - 

35 

70 

io5 

i4o 

176 

2IO 

245 

280 

3i5 

348 

35 

70 

io4 

i3g 

1  74 

209 

244 

278 

3i3 

346 

35 

69 

io4 

1  38 

i73 

208 

242 

277 

3n 

344 

34 

69 

io3 

i38 

172 

2O6 

241 

276 

3io 

342 

34 

68 

io3 

i37 

171 

206 

239 

274 

3o8 

34o 

34 

68 

102 

1  36 

170 

2O4 

238 

272 

3o6 

338 

34 

68 

101 

1  35 

169 

203 

237 

270 

3o4 

336  ' 

34 

67 

101 

1  34 

168 

202 

235 

269 

302 

334  . 

33 

67 

IOO 

1  34 

167 

2OO 

234 

267 

3oi 

332  g 

33 

66 

IOO 

i33 

166 

I99 

232 

266 

299 

• 

33o  - 

33 

66 

99 

132 

i65 

198 

23l 

264 

297 

0 

328  ~ 

33 

66 

98 

i3i 

1  64 

I97 

230 

262 

296 

H 

<D 
V.  * 

326  a  < 

o 

33 

65 

98 

i3o 

i63 

196 

228 

261 

293 

| 

324  £ 

32 

65 

97 

i3o 

162 

194 

227 

269 

292 

P 

322  a 

32 

64 

97 

129 

161 

193 

225 

268 

290 

320   2 

32 

64 

96 

128 

1  60 

I92 

224 

266 

288 

3x8  * 

32 

64 

96 

127 

169 

I9I 

223 

264 

286 

3i6 

32 

63 

95 

126 

168 

I90 

221 

253 

284 

3i4 

3i 

63 

94 

126 

167 

188 

22O 

261 

283 

312 

3i 

62 

94 

125 

1  56 

187 

218 

260 

281 

3io 

3i 

62 

93 

124 

i55 

186 

2I7 

248 

279 

3o8 

3i 

62 

92 

123 

i54 

i85 

216 

246 

277 

3o6 

3i 

61 

92 

122 

i53 

i84 

214 

245 

275 

3o4 

3o 

61 

91 

122 

162 

182 

213 

243 

274 

302 

3o 

60 

91 

121 

161 

181 

211 

242 

272 

3oo 

3o 

60 

9° 

120 

i5o 

180 

2IO 

240 

27O 

298 

3o 

60 

89 

119 

149 

179 

209 

238 

268 

296 

3o 

69 

89 

118 

i4« 

178 

2O7 

237 

266 

294 

I  29 

69 

88 

118 

i47 

176 

206 

235 

266 

LOGARITHMS    OF    NUMBERS. 


N. 

0 

1 

2 

3 

4     5 

6 

7 

8 

9 

D. 

i49 

178186 

3478 

3769 

4o6o 

435i 

464i 

4982 

6222 

55i2 

58o2 

291 

i5o 

6091 

638i 

6670 

6969 

7248 

7536 

7826 

8ii3 

84oi 

8689 

289 

161 

8977 

9264 

9662 

9839 

.126 

.4i3 

.699 

.986 

1272 

i558 

287 

162 

181844 

2129 

2416 

2700 

2985 

3270 

3555 

3839 

4l23 

4407 

286 

i53 

4691 

4976 

6269 

5542 

6826 

6io"8 

6891 

6674 

6966 

7239 

283 

1  54 

7521 

78o3 

8o84 

8366 

8647 

8928 

9209 

9490 

9771 

..5i 

281 

i55 

190332 

0612 

0892 

1171 

i45i 

1780 

2010 

2289 

.2667 

2846 

279 

1  56 

3i25 

34o3 

368i 

3959 

4237 

45i4 

4792 

6069 

5346 

5623 

278 

167 

6900 

6176 

6453 

6729 

7006 

7281 

7556 

7832 

8107 

8382 

276 

168 

8657 

8932 

9206 

948i 

9755 

..29 

.3o3 

.577 

.85o 

1124 

274 

169 

201897 

1670 

1943 

2216 

2488 

2761 

3o33 

33o5 

3577 

3848 

272 

1  60 

4l20 

439i 

4663 

4934 

6204 

5475 

5746 

6016 

6286 

6556 

271 

161 

6826 

7096 

7866 

7634 

79o4 

8i73 

844i 

87io 

8979 

9247 

260. 

162 

95i5 

9783 

..5i 

.819 

.586 

.853 

I  121 

-388 

i654 

1921 

267 

i63 

212188 

2454 

2720 

2986 

3262 

35x8 

3  7.8  3 

4049 

43i4 

4579 

266 

1  64 

4844 

6109 

5373 

5638 

6902 

6166 

643o 

6694 

6967 

7221 

264 

i65 

7484 

7747 

8010 

8273 

8536 

8798 

9060 

9823 

9686 

9846 

262 

166 

220108 

0870 

o63i 

0892 

u53 

i4i4 

1676 

i936 

2196 

2456 

261 

167 

2716 

2976 

3236 

3496 

3755 

4oi5 

4274 

4533 

4792 

5o5i 

269 

1  68 

5309 

5568 

6826 

6o84 

6342 

6600 

6858 

7116 

7372 

7680 

268 

169 

7887 

8:44 

84oo 

8667 

89i3 

9170 

9426 

9682 

9938 

.i93 

266 

170 

280449 

0704 

•0960 

I2l5 

1470 

1724 

1979 

2234 

2488 

2742 

264 

171 

2996 

8260 

35o4 

3757 

4oii 

4264 

45i7 

477o 

5o23 

6276 

253 

172 

5528 

6781 

6o33 

6286 

6687 

6780 

7041 

7292 

7544 

7795 

262 

i73 

8o46 

8297 

8548 

8799 

9049 

9299 

955o 

9800 

..5o 

.3oo 

260 

1  74 

240649 

0799 

"io48 

1297 

1  546 

'795 

2044 

2293 

2641 

279o 

249 

i75 

3o38 

8286 

3534 

3782 

4o3o 

4277 

4525 

4772 

5oi9 

6266 

248 

176 

55i3 

6769 

6006 

6262 

6499 

6745 

6991 

7237 

7482 

7728 

246 

177 

79?3 

8219 

8464 

8709 

8954 

9198 

9443 

9687 

9932 

.176 

245 

178 

260420 

0664 

0908 

1161 

1896 

i638 

1881 

2126 

2368 

2610 

243 

179 

2853 

3096* 

3338 

358o 

3822 

4o64 

43o6 

4548 

479° 

5o3i 

242 

180 

5273 

55i4 

5755 

6996 

6237 

6477 

6718 

6968 

7i98 

7439 

Mi 

181 

7679 

7918 

8i58 

8398 

8637 

8877 

9116 

9833 

239 

N.    0 

1 

2 

3 

4 

5 

6 

7  |  8 

9  |  D. 

292 

29 

58 

88 

117 

1  46 

176 

204 

234 

268 

290 

29 

58 

87 

116 

1  45 

i74 

203 

232 

261 

288 

29 

58 

86 

n5 

1  44 

i73 

2O2 

230 

269 

286 

29 

57 

86 

n4 

i43 

172 

2OO 

229 

257 

284 

28 

$7 

85 

n4 

1  42 

170 

199 

227 

266 

282 

28 

56  • 

85 

n3 

i4i 

169 

197 

226 

264 

280 

28 

56 

84 

112 

i4o 

168 

196 

224 

262 

278 

28 

56 

83 

XII 

I  So 

167 

196 

223 

260 

276 

28 

55 

83 

no 

1  38 

iCG 

198 

221 

274  ,5 

27 

55 

82 

no 

i37 

i64 

191 

2I9 

247 

272  £ 

27 

54 

82 

109 

1  36 

i63 

218 

245 

t 

270  ^ 

27 

54 

81 

1  08 

1  35 

162 

216 

243 

3 

268  i 

27 

54 

80 

107 

1  34 

161 

2*4 

241 

o>  . 
$^ 

266  =« 

27 

53 

80 

106 

i33 

1  60 

186 

213 

239 

| 

264  t» 

26 

53 

79 

1  06 

iSa 

168 

186 

211 

238 

& 

262  £ 

26 

52 

79 

106 

i3i 

167 

i83 

210 

236 

260  g 

26 

52 

78 

io4 

i3o 

i56 

182 

208 

s34 

258  * 

26 

52 

77 

io3 

129 

i55 

181 

2O6 

232 

266 

26 

5i 

77 

102 

128 

1  54 

1-79 

206 

230 

264 

25 

5i 

76 

IO2 

127 

162 

i78 

203 

229 

262 

25 

5o 

76 

101 

126 

161 

176 

202 

227 

260 

26 

5o 

75 

IOO 

125 

160 

176 

2OO 

225 

248 

25 

5o 

74 

99 

124 

149 

x?4 

I98 

223 

246 

25 

49 

74 

98 

123 

i48 

172 

I97 

221 

a44 

24 

49 

73 

98 

122 

i46 

171 

i95 

22O 

<  142 

24 

48 

73 

97 

121 

i45 

169 

i94 

218 

*4o 

24 

48 

72 

96 

I2O 

1  44 

168 

I9a 

216 

LOGARITHMS    OF   NUMBERS. 


N. 

0 

1 

2 

3 

4  1   5 

6 

7 

8 

9 

D. 

182 

260071 

o3io 

o548 

0787 

1025 

1263 

i5oi 

1739 

10,76 

22l4 

238 

i83 

2461 

2688 

2925 

3:62 

3399 

3636 

3873 

4109 

4346 

4582 

237 

1  84 

48i8 

5o54 

5290 

5525 

576i 

5996 

6232 

6467 

6702 

6937 

235 

i85 

7172 

7406 

764i 

7875 

8110 

8344 

8578 

8812 

9o46 

9279 

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186 

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1609 

233 

187 

271842 

2074 

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188 

4i58 

4389 

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6002 

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189 

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207 

6970 

6180 

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7436 

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8o63 

8272 

848  1 

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208 

209 

32oi46 

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0769 

0977 

1184 

i39i 

iSgS 

i8o5 

2OI2 

207 

210 

2219 

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4077 

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211 

4282 

4488. 

4694 

4899 

5io5 

53io 

55i6 

572i 

5926 

6i3i 

2O5 

212 

6336 

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6745 

6950 

7i55 

7359 

7563 

7767 

7972 

8176 

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8583 

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2034 

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2842 

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4o5i 

4253 

202 

216 

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4655 

4856 

5o57 

5257 

5458 

5658 

5859 

6o59 

6260 

2OI 

217 

646o 

6660 

6860 

7060 

7260 

7459 

7659 

7858 

8o58 

8257 

2OO 

2I8 

8456 

8656 

8855 

9054 

9253 

945i 

965o 

9849 

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I99 

219 

34o444 

0642 

0841 

io39 

1237 

i435 

i632 

i83o 

2028 

2225 

I98 

220 

2423 

2620 

2817 

3oi4 

3212 

34o9 

36o6 

38o2 

3999 

4i96 

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0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

238 

'  24 

48 

7i 

95 

^i9 

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167 

I9O 

214 

236 

24 

47 

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94 

118 

i4a 

i65 

189 

212 

234 

23 

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70 

94 

117 

i4o 

1  64 

187 

211 

232 

23 

46 

70 

93 

lie 

i39 

162 

186 

209 

230 

23 

46 

69 

92 

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i38 

161 

1  84 

207 

228 

23 

46 

68 

91 

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i37 

160 

182 

205 

226 

23 

45 

68 

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181 

203 

224   » 

22 

45 

67 

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112 

1  34 

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179 

2O2 

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222   e3 

22 

44 

67 

89 

III 

i33 

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178 

2OO 

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22 

44 

66 

88 

no 

132 

1  54 

176 

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218  °< 

22 

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65 

87 

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216  1 

22 

43 

65 

86 

1  08 

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i5i 

I73 

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214   & 

21 

43 

64 

86 

107 

128 

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i7i 

I93 

212   £ 

21 

42 

64 

85 

106 

127 

i48 

I7O 

I9i 

210 

21 

42 

63 

84 

io5 

126 

i47 

1  68 

i89 

208 

21 

42 

62 

83 

104 

125 

i46 

166 

187 

206 

21 

4i 

62 

82 

io3 

124 

1  44 

i65 

i85 

2O4 

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61 

82 

IO2 

122 

i43 

i63 

1  84 

2O2 

20 

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61 

81 

IOI 

121 

i4i 

162 

182 

200 

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60 

80 

100 

120 

i4o 

1  60 

1  80 

198 

2O 

4o 

59 

79 

99 

II9 

i39 

1  58 

178 

LOGARITHMS    OP    .NUMBERS. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

221 

344392 

4589 

4785 

498i 

5178 

5374 

557o 

5766 

5962 

6i57 

i96 

.  222 

6353 

6549 

6744 

6939 

7i35 

733o 

7525 

7720 

79i5 

8110 

i95 

223 

83o5 

85oo 

8694 

8889 

9o83 

9278 

9472 

9666 

986o 

..54 

1  94 

224 

35o248 

0442 

o636 

o829 

1023 

1216 

i4io 

i6o3 

i796 

1989 

i93 

225 

2i83 

2375 

2568 

2761 

2954 

3i47 

3339 

3532 

3724 

39i6 

226 

4io8 

43oi 

4493 

4685 

4876 

5o68 

5260 

5452 

5643 

5834 

192 

227 

6026 

621-7 

64o8 

6599 

679o 

6981 

7172 

7363 

7554 

7744 

191 

228 

7935 

8i25 

83i6 

85o6 

8696 

8886 

9o76 

9266 

9456 

9646 

I90 

229 

-9835 

..25 

.215 

•  4o4 

.593 

.783 

•972 

1161 

i35o 

i539 

189 

230 

36i728 

191-7 

2105 

2294 

2482 

2671 

2859 

3o48 

3236 

3424 

188 

23l 

36i2 

38oo 

3988 

4176 

4363 

455i 

4739 

4926 

5u3 

53oi 

232 

5488 

5675 

5862 

6o49  6236 

6423 

6610 

6796 

6983 

7l69 

187 

233 

7356 

7542 

7729 

79i5 

8101 

8287 

8473 

8659 

8845 

186 

234 

9216 

9401 

9587 

9772 

9958 

.143 

.328 

.5i3 

.698 

.883 

i85 

235 

37io68 

1253 

i437 

1622 

1806 

1991 

2175 

236o 

2544 

2728 

1  84 

236 

2912 

3096 

328o 

3464 

3647 

383i 

4oi5 

4i98 

4382 

4565 

237 

4748 

4932 

5u5 

5298 

548i 

5664 

5846 

6o29 

6212 

6394 

i83 

238 

6577 

6759 

6942 

7124 

73o6 

7488 

7670 

7852 

8o34 

8216 

182 

239 

8398 

858o 

8761 

8943 

9I24 

93o6 

9487 

9668 

9849 

..3o 

181 

240 

38o2ii 

o392 

o573 

o754 

o934 

in5 

I296 

1476 

i656 

i837 

241 

2017 

2197 

2377 

2557 

2737 

2917 

3o97 

3277 

3456 

3636 

180 

242 

38i5 

3995 

4i74 

4353 

4533 

4712 

489i 

5070 

5249 

5428 

I79 

243 

56o6 

5785 

5964 

6142 

632i 

6499 

6677 

6856 

7o34 

•7212 

178 

344 

739o 

7568 

7746 

7923 

-8101 

8279 

8456 

8634 

8811 

8989 

245 

9166 

9343 

9520 

9698 

9875 

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177 

246 

390935 

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1288 

i46£ 

i64i 

1817 

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2i69 

2345 

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247 

269-7 

2873 

3o48 

3224 

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3575 

3751 

3926 

4ioi 

4277 

248 

4452 

462-7 

4802 

4977 

5i52 

5326 

55oi 

5676 

585o 

6o25 

i75 

249 

6199 

6374 

6548 

6722 

6896 

7071 

7245 

74i9 

7592 

7766 

174 

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8n4  828-7 

846  1 

8634 

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9i54 

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9674 

9847  ..20 

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3293 

3464 

3635 

3807 

3978 

4i49 

4320 

4492 

4663 

1-71 

254 

48,34 

5oo5 

5i76 

5346 

55i7 

5688 

5858 

6o29 

6i99 

637o 

255 

654o 

6710 

6881 

7o5i 

7221 

739I 

756i 

7731 

79oi 

80-70 

170 

256 

8240 

84io  8579 

8749 

89i8 

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0.426 

9595 

9764 

i69 

257 

9933 

.102   .271 

•  44o 

.6o9 

•777 

•  946 

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1283 

i45i 

258 

411620 

1788  i956 

2124 

2293 

2461 

2629 

2796 

2964 

3i32 

168 

259 

33oo 

3467  3635 

38o3 

3970 

4i37 

43o5 

4472 

4639 

48o6 

167 

260 

4973 

5i4o  53o7 

5474 

564i 

58o8 

5974 

6i4i 

63o8 

6474 

261 

664i 

680-7  6973 

7i39 

73o6 

7472 

7638 

7804 

7970 

8i35 

1  66 

262 

83oi 

8467  :  8633 

8798 

8964 

9I29 

9295 

946o 

9625 

9791 

i65 

263 

9956 

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.45i 

.616 

.781 

.945 

II  IO 

1275 

i439 

N. 

G 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

196 

20 

39 

59 

78 

98 

118 

i37 

i57 

176 

194 

J9 

39 

58 

78 

97 

116 

1  36 

i55 

i75 

192 

i9 

38 

58 

77 

96 

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1  34 

1  54 

i73 

190 

i9 

38 

57 

76 

95 

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1  33 

1  59 

171 

188 

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38 

56 

75 

94 

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i5o 

169 

186  g 

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37 

56 

74 

93 

112 

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1  49 

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1  84  c£ 

18 

37 

55 

74 

92 

110 

129 

i47 

166 

0 

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182  -3 

18 

36 

55 

73 

91 

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12-7 

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1  64 

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180  §  « 

18 

36 

54 

72 

1  08 

126 

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162 

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178  £ 

18 

36 

53 

71 

89 

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125 

1  49 

1  60 

s 

176  g. 

18 

35 

53 

70 

88 

106 

123 

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1  58 

174  Pk 

17 

35 

52 

70 

87 

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122 

1  39 

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172 

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34 

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69 

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1  38 

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170 

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34 

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68 

85 

102 

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1  68 

17 

34 

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67 

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118 

1  34 

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1  66 

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66 

83 

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116 

i33 

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Ii64 

16 

33 

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66 

82 

98 

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1  48 

LOGARITHMS    OF    NUMBERS. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

264 

421604 

1768 

1933 

2097 

2261 

2426 

259o 

2754 

29l8 

3o82 

1  64 

265 

3246 

34io 

3574 

3737 

39oi 

4o65 

4228 

4392 

4555 

4718 

266 

4882 

5o45 

5208 

537i 

5534 

5697 

586o 

6023 

6186 

6349 

i63 

267 

65ii 

6674 

6836 

6999 

7161 

7324 

7486 

7648 

7811 

7973 

162 

268 

8i35 

8297 

8459 

8621 

8783 

8944 

9io6 

0,268 

9429 

959i 

269 

9752 

9914 

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.236 

.398 

.559 

.720 

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1203 

161 

270 

43i364 

i525 

i685 

1846 

2007 

2167 

2328 

2488 

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28o9 

271 

2969 

3i3o 

3290 

345o 

36io 

377o 

393o 

4o9o 

4249 

44o9 

1  60 

272 

4569 

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4888 

5o48 

5207 

5367 

5526 

5685 

5844 

6oo4 

169 

273 

6i63 

6322 

648  1 

664o 

6799 

6957 

7116 

7275 

7433 

7592 

274 

775i 

7909 

8067 

8226 

8384 

8542 

8701 

8859 

9oi7 

9J75 

1  58 

276 

9333 

9491 

9648 

9806 

9964 

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•  594 

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276 

440909 

1066 

1224 

1  38  1 

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i852 

20O9 

2166 

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277 

2^80 

2637 

2793 

295o 

3io6 

3263 

34i9 

3576 

3732 

3889 

278 

4o45 

4201 

4357 

45i3 

4669 

4825 

4g8i 

5i37 

5293 

5449 

i56 

279 

56o4 

5760 

59i5 

6o7i 

6226 

6382 

6537 

6692 

6848 

7003 

i55 

280 

7i58 

73i3 

7468 

7623 

7778 

7933 

8088 

8242 

8397 

8552 

281 

8706 

8861 

9015 

9170 

9324 

9478 

9633 

9787 

994i 

..95 

1  54 

282 

450249 

o4o3 

o557 

0711 

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1018 

1172 

i326 

i479 

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283 

1786 

1940 

2093 

2247 

2400 

2553 

2706 

2859 

3012 

3i65 

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284 

33i8 

347i 

3624 

3777 

393o 

4082 

4235 

4387 

454o 

4692 

286 

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4997 

5i5o 

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59io 

6062 

6214 

I  52 

286 

6366 

65i8 

6670 

6821 

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287 

7882 

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288 

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1  348 

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290 

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291 

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4042 

4191 

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4490 

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292 

5383 

5532 

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5829 

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6126 

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6719 

298 

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1  48 

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43 

57 

7i 

85 

99 

n4 

128 

i4o     1  4 

28 

42 

56 

70 

84 

98 

112 

126 

LOGARITHMS    OF    NUMBERS. 


N. 

0 

I    2 

3 

4 

5 

6 

7 

8 

9 

D. 

312 

494i55 

4294 

4433 

4572 

4711 

485o 

4989  0128 

5267 

54o6 

i39 

3i3 

5544 

5683 

5822 

596o 

6o99 

6238 

6376  65i5 

6653 

679i 

3i4 

693o 

-7068 

7206 

7344 

7483 

7621 

7759  7897 

8o35 

8i73 

1  38 

3i5 

83n 

8448 

8586 

8724 

8862 

8999 

9i37  9275 

9412 

955o 

3i6 

9687 

9824 

9962 

••99 

.236 

.374 

.5n  .648 

.785 

.922 

i37 

3i7 

5oio59 

n96 

i333 

i47o 

i6o7 

1  744 

i860  !  20I7 

2i54 

229I 

3i8 

2427 

2564 

2700 

2837 

2973 

3109 

3246 

2382 

35i8 

3655 

i36 

3i9 

379i 

3927 

4o63 

4199 

4335 

4471 

4607 

4743 

4878 

5oi4 

320 

5i5o 

5286 

5421 

5557 

5693 

5828 

5964 

6o99 

6234 

637o 

321 

65o5 

664o 

6776 

69n 

7o46 

7181 

73i6 

745i 

7586 

772i 

i35 

322 

7856 

799  1 

8126 

8260 

8395 

853o 

8664 

8799 

8934 

9o68 

323 

92o3 

9337 

9471 

96o6 

974o 

9874 

.  .  .9 

.i43 

•277 

.4n 

1  34 

324 

5io545 

o679 

o8i3 

o947 

1081 

I2l5 

i349 

1482 

1616 

i75o 

325 

i883 

2OI7 

2l5l 

2284 

2418 

255i 

2684 

2818 

295i 

3o84 

i33 

326 

32i8 

335i 

3484 

36i7 

375o 

3883 

4oi6 

4i49 

4282 

44i5 

327 

4548 

468  1 

48i3 

4946 

5o79 

5211 

5344 

5476 

56o9 

574i 

328 

5874 

6006 

6i39 

627I 

64o3 

6535 

6668 

6800 

6933 

7o64 

132 

329 

-7196 

7328 

7460 

7592 

7724 

7855 

7987 

8ii9 

825i 

8382 

33o 

85i4 

8646 

8777 

89o9 

9o4o 

9171 

93o3 

9434 

9566 

9697 

i3i 

33i 

9828 

9959 

..9o 

.221 

.353 

•  484 

.6i5 

.745 

.876 

I007 

332 

52ii38 

I269 

i4oo 

i53o 

1661 

1792 

I922 

2o53 

2i83 

23l4 

333 

2444 

2575 

27o5 

2835 

2966 

3096 

3226 

3356 

3486 

36i6 

i  So 

334 

3746 

3876 

4oo6 

4:36 

4266 

4396 

4526 

4656 

4785 

49i5 

335 

5o45 

5i74 

53o4 

5434 

5563 

5693 

5822 

595i 

6081 

6210 

I29 

336 

6339 

6469 

6598 

6727 

6856 

6985 

7n4 

7243 

7372 

75oi 

337" 

763o 

7759 

7888 

8016 

8i45 

8274 

8402 

853i 

8660 

8788 

338 

89i7 

9o45 

9i74 

93C2 

943o 

9559 

9687 

98  i  5  9943 

..72 

128 

339 

53o2oo 

o328 

o456 

o584 

07I2 

o84o 

o968 

1096 

1223 

i35i 

34o 

i479 

i6o7 

i734 

1862 

I990 

2117 

2245 

2372 

2500 

2627 

34i 

2754 

2882 

3oo9 

3i36 

3264 

339i 

35i8 

3645 

3772 

3899 

I27 

342 

4026 

4i53 

4280 

44o7 

4534 

466i 

4787 

4914 

5o4i 

5i67 

343 

5294 

542i 

5547 

5674 

58oo 

5927 

6o53 

6180 

63o6 

6432 

126 

344 

6558 

6685 

6811 

6937 

7o63 

7i89 

73i5 

744i 

7567 

7693 

345 

7819 

7945 

8o7i 

8i97 

8322 

8448 

8699  8825 

895i 

346 

9076 

92O2 

9327 

9452 

9578 

97°3 

9829  9954  .  .79 

.204 

125 

347 

54o329 

o455 

o58o 

o7o5 

o83o 

o955 

1080  i2o5 

i33o 

1454 

348 

i579 

i7o4 

i829 

i953 

2078 

22O3 

2327 

2452 

2576 

27OI 

349 

2825 

295o 

3o74 

3i99 

3323 

3447 

357i 

3696 

3820 

3944 

124 

35o 

4o68 

4l92 

43i6 

444o 

4564 

4688 

4812 

4936 

5o6o 

5i83 

35i 

53o7 

543  1 

5555 

5678 

58o2 

5925 

6o49 

61-72 

6296 

64i9 

352 
353 

6543 
7775 

6666 
7808 

6789 
8021 

69i3 

8i44 

7o36 

8267 

7i59 
8389 

-7282 
85i2 

74o5 
8635 

I'll 

7652 

8881 

123 

354 

9oo3 

9I26 

9249 

937i 

9494 

96i6 

9739 

9861 

9984 

.106 

355 

550228 

o35i 

o473 

o595 

07I7 

o84'o 

O962 

io84 

1206 

i328 

122 

356 

i45o 

1572 

i694 

1816 

i938 

2060 

2181 

23o3 

2425 

2547 

357 

2668 

2790 

29II 

3o33 

3i55 

3276 

3398  i  35i9  364o 

3762 

121 

358 

3883 

4oo4 

4126 

4247 

4368 

4489 

46io  473i  4852 

4973 

359 

5o94 

52i5 

5336 

5457 

5578 

5699 

5820  594o  6061 

6182 

36o 

63o3 

6423 

6544 

6664 

6785 

-7026  7i46  7267 

7387 

120 

36i 

75o7 

7627 

7748 

-7868- 

7988 

"8108 

8228  '  8349  8469 

8589 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

1  38 

i4 

28 

4i 

55 

6^ 

8.3 

97 

IIQ 

124 

i36  oj 

i4 

27 

4i 

54 

68 

82 

95 

109 

122 

1  34  S 

i3 

27 

4o 

54 

67 

80 

94 

10-7 

121 

• 

132  PL- 

i3 

26 

4o 

53 

66 

79 

92 

!06 

119 

c 

i3o  "5 

i3 

26 

39 

52 

65 

78 

91 

io4 

l!7 

1  ' 

128  |' 

i3 

26 

38 

Si 

64 

77 

9° 

1  02 

Il5 

5 

126  o 

i3 

25 

38 

5o 

63 

76 

88 

101 

n3 

P 

124  f 

12 

25 

37 

5o 

62 

74 

87 

99 

112 

1122  £ 

12 

24 

37 

49 

61 

73 

85 

98 

110 

120 

12 

24 

36 

48 

60 

72 

84* 

96 

1  08 

LOGARITHMS    OF    NUMBERS. 


.  N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

;  362 

5587o9 

8829 

8948 

9068 

9i88 

93o8 

9428 

9548 

9667 

9787 

120 

363 

9907 

..26 

.i46 

.265 

.385 

.5o4 

.624 

.743 

.863 

.9&2 

364 

56noi 

1221 

i34o 

i459 

1578 

i698 

1817 

1936 

2o55 

2I74 

1I9 

365 

2293 

24l2 

253i 

265o 

2769 

2887 

3oo6 

3i25 

3244 

3362 

366 

348i 

36oo 

37i8 

3837 

3955 

4o74 

4l92 

43n 

4429 

4548 

567 

4666 

4784 

4903 

5O2I 

5i39 

5257 

5376 

5494 

56i2 

•573o 

118 

368 

5848 

5966 

6o84 

6202 

6320 

6437 

6555 

6673 

679,1 

69o9 

369 

7026 

7i44 

7262 

7379 

7497 

76i4 

7732 

7849 

7967 

8084 

37o 

8202 

8319 

8436 

8554 

867I 

8788 

89o5 

9023 

9i4o 

9257 

117 

37i 

9374 

9491 

9608 

9725 

9842 

9959 

..76 

.193 

.3o9 

.426 

372 

57o543 

0660 

0776 

o893 

IOIO 

1126 

1243 

1359 

1476 

l592 

373 

I7°9 

1825 

2o58 

2I74 

229I 

2407 

2523 

2639 

2755 

116 

374 

2872 

2988 

3io4 

3220 

3336 

3452 

3568 

3684 

38oo 

39i5 

375 

4o3i 

4i47 

4263 

4379 

4494 

46io 

4726 

484i 

4957 

5o72 

376 

5i88 

53o3 

54i9 

5534 

565o 

5765 

588o 

5996 

6m 

6226 

n5 

377 

634i 

6457 

6572 

6687 

6802 

69i7 

7o32 

7i47 

7262 

7377 

378 

7492 

7607 

7722 

7836 

795i 

8066 

8181 

8295 

84io 

8525 

379 

8639 

8754 

8868 

8983 

9°97 

O2I2 

9326 

944i 

9555 

9669 

n4 

38o 

9784 

9898 

.  .12 

.  126 

.241 

.355 

•  469 

.583 

.697 

.811 

38i 

58o925 

1039 

u53 

1267 

i38i 

i495 

1608 

I722 

i835 

i95o 

382 

2o63 

2I77 

2291 

2404 

25i8 

263i 

2745 

2858 

2972 

3o85 

383 

3io9 

33i2 

3426 

N3539 

3652 

3765 

3879 

3992 

4io5 

4218 

n3 

384 

433i 

4444 

4557 

4670 

4783 

4896 

5oo9 

5l22 

5235 

5348 

385 

546i 

5574 

5686 

5799 

59I2 

6024 

6i37 

625o 

6362 

6475 

386 

6587 

6700 

6812 

6925 

7o37 

7i49 

•7262 

7374 

7486 

7599 

112 

387 

7711 

7823 

7935 

8047 

8160 

8272 

8384 

8496 

8608 

8720 

388 

8832 

8944 

9o56 

9l67 

9279 

939i 

95o3 

96i5 

9726 

9838 

389 

995o 

..61 

.I73 

.284 

.396 

.5o7 

.6i9 

.73o 

.842 

.953 

Sgo 

59io65 

1176 

1287 

i399 

i5io 

1621 

I732 

i843 

i955 

2066 

III 

391 

2177 

2288 

2399 

25lO 

2621 

2732 

2843 

2954 

3o64 

3i75 

392 

3286 

3397" 

3  5  08 

36i8 

3729 

384o 

395o 

4o6i 

4i7i 

4282 

393 

4393 

45o3 

46i4 

4724 

4834 

4945 

5o55 

5i65 

5276 

5386 

110 

394 

5496 

56o6 

6717 

5827 

5937 

6047 

6i57 

6267 

6377 

6487 

395 

6597 

6707 

6817 

6927 

7o37 

7146 

7256 

7366 

7476 

7586 

396 

7695 

78o5 

79i4 

8024 

8i34 

8243 

8353 

846a 

8572 

8681 

397 

879i 

8900 

9009 

9119- 

0.228 

9337 

9446 

9556 

9665 

9774 

100 

398 

9883 

9992 

.101 

.210 

.319 

.428 

.537 

.646 

.755 

.864 

399 

6oo973 

1082 

1191 

I299 

i4o8 

i5i7 

1620 

1734 

i843 

i95r 

4oo 

2060 

2169 

2277 

2386 

2494 

a6o3 

27II 

28i9 

2928 

3o36 

108 

4oi 

3i4'4 

3253 

336i 

3469 

3577 

3686 

3794 

3902 

4oio 

4n8 

4O2 

4226 

4334 

4442 

455o 

4658 

4766 

4874 

4982 

5089 

5i97 

4o3 

53o5 

54i3 

552i 

5628 

5736 

5844 

595i 

6o59 

6166 

6274 

4o4 

638i 

6489 

6596 

6704 

6811 

69i9 

7026 

7i33 

•7241 

7348 

io7 

4o5 

7455 

7562 

7669 

7777 

7884 

7991 

8o98 

82o5 

83i2 

8419 

4o6 

8526 

8633 

874o 

8847 

8954 

9o6i 

9167 

9274 

938i 

9488 

4o7 

9594 

9701 

9808 

99i4  ..21 

.128 

.234 

.34i 

•  447 

.554 

4o8 

610660 

0767 

0873 

o979  1086 

II92 

1298 

i4o5 

i5n 

i6i7 

1  06 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

•  8 

9 

D. 

n9 

12 

24 

36 

48 

60 

7J 

83 

95 

10-7 

118 

12 

24 

35 

47 

59 

71 

83 

94 

1  06 

"7  . 

12 

23 

35 

47 

59 

70 

82 

94 

io5 

"6  fi 

12 

23 

35 

46 

58 

70 

81 

93 

io4 

o5 

115  1 

12 

23 

35 

46 

58 

69 

81 

-93 

io4 

s 

u4  « 

II 

23 

34 

46 

57 

68 

80 

91 

io3 

i- 

n3  |  . 

II 

23 

34 

45 

57 

68 

79 

9° 

1  02 

5§ 

112  £ 

II 

22 

34 

45 

56 

67 

78 

90 

101 

ft 

III   0, 

II 

22 

33 

44 

56 

67 

78 

89 

100 

no  2 

II 

22 

33 

44 

55 

66 

77 

88 

99 

109  ^ 

II 

22 

33 

44 

55 

65 

76 

87 

98 

1  08 

II 

22 

32 

43 

54 

65 

76 

86 

97 

107 

II 

21 

32 

43 

54 

64' 

75 

86 

96 

to 


LOGARITHMS    OP   NUMBERS. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

409 

611723 

1829 

1936 

2O42 

2i48 

2254 

236o 

2466 

2572 

2678 

106 

4io 

2784 

2890 

2996 

3102 

3207 

33i3 

3419 

3525 

363o 

3736 

4n 

3842 

3947 

4o53 

4i59 

4264 

437o 

44?5 

458i 

4686 

4792 

412 

4897 

5oo3 

5io8 

52i3 

5319 

5424 

5529 

5634 

574o 

5845 

io5 

4i3 

5950 

6o55 

6160 

6265 

637o 

6476 

658i 

6686 

6790 

6895 

4U 

7000 

7io5 

7210 

73i5 

7420 

7525 

7629 

7734 

7839 

7943 

4i5 

8o48 

8i53 

8257 

8362 

8466 

857i 

8676 

8780 

8884 

8989 

4i6 

9°93 

9198 

9302 

9406 

95i  i 

96i5 

9719 

0.824 

9928 

..32 

104 

4i7 

62oi36 

O24o 

o344 

0448 

o552 

o656 

0760 

o864 

0968 

1072 

4i8 

1176 

1280 

1  384 

i486 

l592 

i695 

1799 

I9o3 

2007 

2110 

419 

22l4 

23i8 

2421 

2525 

2628 

2732 

2835 

2939 

3o42 

3i46 

420 

3249 

3353 

3456 

3559 

3663 

3766 

3869 

3973 

4076 

4179 

io3 

421 

4282 

4385 

4488 

459i 

4695. 

4798 

4901 

5oo4 

5107 

5210 

422 

53i2 

54i5 

55i8 

562i 

5724 

5827 

5929 

6o32 

6i35 

6238 

423 

634o 

6443 

6546 

6648 

675i 

6853 

6956 

7o58 

7161 

7263 

424 

7366 

7468 

757i 

7673 

7775 

7878 

7980 

8082 

8i85 

8287 

IO2 

426 

8389 

8491 

8593 

8695 

8797 

89oo 

9002 

9io4 

9206 

93*8 

426 

9410 

9512 

96i3 

97i5 

0817 

99i9 

.  .2.1 

.123 

.224 

.326 

427 

63o428 

o53o 

o63i 

o733 

o835 

o936 

io38 

n39 

1241 

1  342 

428 

1  444 

1  545 

1647 

1748 

i849 

i95i 

2062 

2i53 

2255 

2356 

101 

429 

2457 

2559 

2660 

2761 

2862 

2963 

3o64 

3i65 

3266 

3367 

43o 

3468 

3569 

3670 

377i 

3872 

3973 

4074 

4i75 

4276 

4376 

43i 

4477 

4578 

4679 

4779 

488o 

498i 

5o8i 

5i82 

5283 

5383 

IOO 

432 

5484 

5584 

5685 

5785 

5886 

5986 

6087 

6i87 

6287 

6388 

433 

6488 

6588 

6688 

6789 

6889 

6989 

7089 

7i89 

7290 

739o 

434 

7490 

759° 

7690 

779° 

789o 

799° 

8090 

8i9o 

8290 

8389 

435 

8489 

8589 

8689 

8789 

8888 

8988 

9088' 

9i88 

9287 

9387 

99 

436 

9486 

9586 

9686 

9785 

9885 

9984 

..84 

.i83 

.283 

.382 

437 

64o48i 

o58i 

0680 

0779 

o879 

o978 

1077 

1177 

1276 

i375 

438 

i4?4 

1573 

1672 

1771 

18-71 

i97o 

2069 

2168 

2267 

2366 

439 

2465 

2563 

2662 

2761 

2860 

2959 

3o58 

3i56 

3255 

3354 

44o 

3453 

355i 

365o 

3749 

3847 

3946 

4o44 

4i43 

4242 

434o 

98 

44  1 

4439 

4537 

4636 

4734 

4832 

493i 

5029 

5127 

5226 

5324 

442 

5422 

552i 

56i9 

5717 

58i5 

59i3 

60  1  1 

6110 

6208 

63o6 

443 

64o4 

65o2 

6600 

6698 

6796 

6894 

6992 

7o89 

7187 

7285 

444 

7383 

748  1 

7579 

7676 

7774 

7872 

7969 

8067 

8i65 

8262 

445 

836o 

8458 

8555 

8653 

875o 

8848 

8945 

9o43 

9140 

9237 

97 

446 

9335 

9432 

953o 

9627 

9724 

982I 

99i9 

..16 

.n3 

.210 

447 

65o3o8 

o4o5 

o5o2 

0599 

o696 

o793 

o89o 

o987 

io84 

1181 

448 

1278 

i375 

1472 

i569 

1666 

1762 

i859 

I956 

2o53 

2i5o 

449 

2246 

2343 

2440 

2536 

2633 

2730 

2826 

2923 

3019 

3n6 

45o 

32i3 

33o9 

34o5 

35o2 

3598 

3695 

379i 

3888 

3984 

4o8o 

96 

45  1 

4i77 

4273 

4369 

4465 

4562 

4658 

4?54 

485o 

4946 

5o42 

452 

5:38 

5235 

533i 

5427 

5523 

56i9 

57i5 

58io 

5906 

6002 

453 

6098 

6194 

629.0 

6386 

6482 

6577 

6673 

6769 

6864 

696o 

454 

7o56 

7lf>2 

7247 

7343 

7438 

7534 

7629 

7725 

7820 

79i6 

455 

Sou 

8107 

8202 

8298 

8393 

8488 

8584 

8679 

8774 

8870 

95 

456 

8965 

9060 

9i55 

925o 

9346 

944i 

9536 

963i 

9726 

0.821 

457 

9916 

.  .  ii 

.  106 

.201 

.296 

.39i 

.486 

.58i 

.676 

.771 

N. 

0     1 

2 

3 

4 

5 

6 

7 

8 

9 

1). 

1  06 

ii 

21 

32 

4a 

53 

64 

74 

85 

9b 

io5 

ii 

21 

32 

4a 

53 

63 

74 

84 

95 

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IO 

21 

3i 

42 

52 

62 

73 

83 

94 

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103  £ 

10 

21 

3i 

4i 

52 

62 

72 

82 

93 

05 

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102  „ 

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3i 

4i 

5i 

61 

7i 

82 

93 

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101   |  , 

IO 

20 

3o 

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5i 

61 

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81 

91 

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IO 

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3o 

4o 

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60 

70 

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69 

79 

89 

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29 

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97  P 

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68 

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10 

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29 

38 

48 

58 

67 

77 

86 

Lo-GARITHMS      OF     NUMBERS. 


N."1"  0 

1 

2 

3 

4  ]|  5 

6 

7 

8 

9 

D 

458 

66o865 

o96o 

io55 

n5o 

1245 

i339 

i434 

ID29 

1623 

1718 

95 

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i8i3 

I9o7 

2O02 

2O96 

2I9I 

2286 

238o 

2475 

2569 

2663 

46o 

2758 

2852 

2947 

3o4i 

3  1  35 

323o 

3324 

34i8 

35i2 

3607 

94 

46  1 

3701 

3795 

3889 

3983 

4o78 

4l72 

4266 

436o 

4454 

4548 

462 

4642 

4736 

483o 

4924 

5oi8 

5lI2 

5206 

5299 

5393 

5487 

463 

558i 

5675 

5769 

5862 

5956 

6o5o 

6i43 

6237 

633i 

6424 

464 

65i8 

6612 

6705 

6799 

6892 

6986 

7°79 

7i73 

7266 

736o 

465 

7453 

7546 

7640 

7733 

7826 

7920 

8oi3 

8106 

8i99 

8293 

93 

466 

8386 

8479 

8572 

8665 

8759 

8852 

8945 

9o38 

9i3i 

9224 

467 

93i7 

94io 

95o3 

9596 

9689 

9782 

9875 

9967 

..60 

,i53 

468 

670246 

oSSg 

o43i 

o524 

061-7 

07IO 

0802 

o895 

o988 

1080 

469 

1173 

1265 

i358 

i45i 

1  543 

i636 

1728 

1821 

I9i3 

2OO5 

47o 

2098 

2190 

2283 

2375 

2467 

256o 

2652 

2744 

2836 

2929 

92 

47i 

3021 

3n3 

32o5 

3297 

339o 

3482 

3574 

3666 

3758 

385o 

472 

3942 

4o34 

4126 

4218 

43io 

4402 

4494 

4586 

4677 

4769 

473 

486i 

4953 

5o45 

5i37 

5228 

5320 

54i2 

55o3 

5595 

5687 

474 

>778 

587o 

5962 

6o53 

6i45 

6236 

6328 

64i9 

65n 

6602 

475 

6694 

6785 

6876 

6968 

7o59 

7i5i 

7242 

-,333 

7424 

75i6 

91 

7607 

•7698 

7789 

7881 

7972 

8o63 

8i54 

8245 

8336 

8427 

477 

85i8 

8609 

8700 

879i 

8882 

8973 

9064 

9i55 

9246 

9337 

478 

9428 

95i9 

9610 

97oo 

9791 

9882 

9973 

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.i54 

.245 

479 

68o336 

0426 

o5i7 

0607 

o698 

o789 

0879 

o97O 

1060 

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48o 

1241 

i332 

l422 

i5i3 

i6o3 

i693 

1784 

i874 

i964 

2o55 

9° 

48  1 

2i45 

2235 

2326 

2416 

25o6 

2596 

2686 

2777 

2867 

2957 

482 

3o47 

3i37 

3227 

33i7 

34o7 

3497 

3587 

3677 

3767 

3857 

483 

3947 

4o37 

4l27 

4217 

43o7 

4396 

4486 

4576 

4666 

4756 

484 

4845 

4935 

5o25 

5n4 

52o4 

5294 

5383 

5473 

5563 

5652 

485 

5742 

583i 

5921 

6010 

6100 

6i89 

6279 

6368 

6458 

6547 

89 

486 

6636 

6726 

68i5 

69o4 

6994 

7o83 

7172 

726l 

735i 

744o 

487 

7529 

7618 

7707 

7796 

7886 

7975 

8o64 

8i53 

8242 

833i 

488 

8420 

8509 

8598 

8687 

8776 

8865 

8953 

9o42 

9i3i 

922O 

489 

93o9 

9398 

9486 

9575 

9664 

9753 

9841 

993o 

.  .19 

.107 

49o 

69oi96 

0285 

0373 

0462 

o55o 

o639 

0728 

0816 

ogoS 

o993 

49i 

1081 

1170 

I258 

i347 

i435 

i524 

1612 

1700 

1789 

1877 

88 

492 

i965 

2o53 

2l42 

2230 

23i8 

2406 

2494 

2583 

2671 

2759 

493 

2847 

2935 

3023 

3m 

3i99 

3287 

3375 

3463 

355i 

3639 

494 

3727 

38i5 

SgoS 

399i 

4o78 

4i66 

4254 

4342 

443o 

45i7 

495 

46o5 

4693 

478l 

4868 

4956 

5o44 

5i3i 

52I9 

5307 

5394 

496 

5482 

5569 

5657 

5744 

5832 

59i9 

6007 

6o94 

6182 

6269 

87 

497 

6356 

6444 

653i 

6618 

67o6 

6793 

6880 

6968 

7o55 

7142 

498 

7229 

73:7 

74o4 

749i 

7578 

7665 

775a 

7839 

7926 

8oi4 

499 

8101 

8188 

8275 

8362 

8449 

8535 

8622 

87o9 

8796 

8883 

5oo 

897o 

9067 

9i44 

923l 

93i7 

94o4 

9491 

9578 

9664 

975i 

5oi 

9838 

9024 

.  .  ii 

..08 

.184 

.271 

.358 

.444 

.53i 

.617 

502 

7oo7o4 

0790 

0877 

oo63 

io5o 

n36 

1222 

i3o9 

iSgS 

1482 

86 

5o3 

i568 

1  654 

1741 

1827 

I9i3 

i999 

2086 

2I72 

2258 

2344 

5o4 

243l 

2517 

26o3 

2689 

2775 

2861 

2947 

3o33 

3119 

32o5 

5o5 

329I 

3377 

3463 

3549 

3635 

3721 

3807 

3893 

3979 

4o65 

5o6 

4i5i 

4236 

4322 

44o8 

4494 

4579 

4665 

475i 

4837 

4922 

507 

5oo8 

5094 

5  1  79 

5265 

535o 

5436 

5522 

56o7 

5693 

5778 

N. 

0 

1 

2 

3 

4   ||   5 

6 

7 

8 

9 

D. 

95 

IO 

19 

29 

38 

48 

57 

67 

76 

86 

94  a 

9 

19 

28 

38 

47 

56 

66 

75 

85 

93  s 

9 

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28 

37 

47 

56 

65 

74 

84 

a 

92  PU 

9 

18 

28 

37 

46 

55 

64 

74 

83 

Q 

£  - 

91  1- 

9 

18 

27 

36 

46 

55 

64 

73 

82 

9°  «   9 

18 

27 

36 

45 

54 

61 

72 

81 

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89  I'  9 

18 

27 

36 

45 

53 

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80 

88  o"   g 

18 

26 

35 

44 

53 

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79 

87  £ 

9 

17 

26 

35 

44 

52 

61 

70 

78 

86 

9 

17 

26 

34 

43 

52 

60 

69 

77 

LOGARITHMS    OF    NUMBERS. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

5o8 

7o5864 

5949 

6o35 

6120 

6206 

6291 

6376 

6462 

6547 

6632 

85 

5o9 

67i8 

68o3 

6888 

6974 

7o59 

7i44 

7229 

73i5 

74oo 

7485 

5io 

757o 

7655 

7740 

7826 

7911 

7996 

8081 

8166 

825x 

8336 

5u 

8421 

85o6 

859i 

8676 

8761 

8846 

893i 

9oi5 

9xoo 

9x85 

5l2 

927o 

9355 

944o 

9524 

9609 

9694 

9779 

9863 

9948 

..33 

5i3 

7IOII7 

O2O2 

0287 

0371 

o456 

o54o 

0625 

0710 

o794 

08  79 

5i4 

o963 

io48 

Il32 

1217 

i3oi 

i385 

1470 

x554 

x639 

1723 

84 

5i5 

i8o7 

l892 

1976 

2060 

2i44 

2229 

23i3 

2397 

248  1 

2566 

5i6 

265o 

2734 

2818 

2902 

2986 

3070 

3i54 

3238 

3323 

34o7 

5i7 

349i 

3575 

3659 

3742 

3826 

3910 

3994 

4078 

4x62 

4246 

5i8 

433o 

44i4 

4497 

458i 

4665 

4749 

4833 

49x6 

5ooo 

5o84 

5i9 

5i67 

525i 

5335 

54i8 

55o2 

5586 

5669 

5753 

5836 

592O 

52O 

6oo3 

6087 

6170 

6254 

6337 

6421 

65o4 

6588 

667x 

6754 

83 

521 

6838 

692I 

7004 

7088 

7171 

7254 

7338 

7421 

75o4 

7587 

522 

7671 

7754 

7837 

7920 

8oo3 

8086 

8i69 

8253 

8336 

84i9 

523 

85o2 

8585 

8668 

875i 

8834 

8917 

9ooo 

9o83 

9i65 

9248 

524 

933i 

94i4 

9497 

9$  So 

9663 

9745 

9828 

99xx 

9994 

••77 

525 

720l59 

0242 

o325 

0407 

0490 

o573 

o655 

o738 

0821 

o9o3 

526 

o986 

1068 

u5i 

1233 

i3i6 

i398 

i48i 

x563 

x  646 

1728 

82 

527 

1811 

i893 

i975 

2o58 

2i4o 

2222 

23o5 

2387 

2469 

2552 

528 

2634 

2716 

2798 

2881 

2963 

3o45 

3127 

3209 

3291 

3374 

529 

3456 

3538 

3620 

3702 

3784 

3866 

3948 

4o3o 

4lI2 

4i94 

53o 

4276 

4358 

444o 

4522 

46o4 

4685 

4767 

4849 

4g3x 

5ox3 

53i 

5o95 

5176 

5258 

534o 

5422 

55c3 

5585 

5667 

5748 

583o 

532 

59I2 

5993 

6o75 

6i56 

6238 

6320 

64oi 

6483 

6564 

6646 

533 

6727 

68o9 

689o 

6972 

7o53 

7i34 

7216 

7297 

7379 

7460 

81 

534 

754i 

7623 

77o4 

7785 

7866 

7948 

8o29 

8110 

8191 

8273 

535 

8354 

8435 

85i6 

8597 

8678 

8759 

884i 

8(,22 

9003 

9084 

536 

9i65 

9246 

9327 

94o8 

9489 

957o 

965i 

973'2 

9813 

9893 

537 

9974 

..55 

.136 

.2I7 

.298 

.378 

•  459 

.540 

.621 

.702 

538 

73o782 

o863 

o944 

1024 

no5 

1186 

1266 

1  347 

1428 

i5o8 

539 

1589 

i669 

i75o 

i83o 

1911 

i99i 

2072 

2l52 

2233 

a3i3 

54o 

2394 

2474 

2555 

2635 

2715 

2796 

2876 

2956 

3o37 

3n7 

80 

54i 

3i97 

3278 

3358 

3438 

35i8 

3598 

3679 

3759 

3839 

39x9 

542 

3999 

4o79 

4x^0 

4240 

4320 

44oo 

448o 

456o 

464o 

4720 

543 

48oo 

488o 

496o 

5o4o 

5l2O 

52OO 

5279 

5359 

5439 

55x9 

544 

5599 

5679 

5759 

5838 

59i8 

5998 

6078 

6i57 

6237 

63i7 

545 

6397 

6476 

6556 

6635 

6715 

6795 

6874 

6954 

7o34 

7n3 

546 

7193 

7272 

7352 

743  1 

75n 

767o 

7749 

7829 

79o8 

79 

547 

7987 

8067 

8i46 

8225 

83o5 

8384 

8463 

8543 

8622 

87ox 

548 

878i 

8860 

8939 

9oi8 

9097 

9i77 

9256 

9335 

94i4 

9493 

549 

9572 

965i 

973i 

98io 

9889 

9968 

..47 

.126 

.2O5 

.284 

55o 

74o363 

0442 

o52I 

0600 

0678 

°757 

o836 

0915 

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xo73 

55i 

Il52 

1230 

1  309 

1  388 

1467 

1  546 

1624 

I7o3 

1782 

1860 

552 

i939 

2018 

2096 

2175 

2254 

2332 

2411 

2489 

2568 

2647 

553 

2725 

2804 

2882 

296i 

3o39 

3n8 

3i96 

3275 

3353 

343  1 

78 

554 

35io 

3588 

3667 

3745 

3823 

39O2 

398o 

4o58 

4x36 

42i5 

555 

4293 

437i 

4449 

4528 

46o6 

4684 

4762 

484o 

49x9 

4997 

556 

5o75 

5i53 

523i 

53o9 

5387 

5465 

5543 

562i 

5699 

5777 

557 

5855 

5933 

6011 

6089 

6167 

6245 

6323 

64ox 

6479 

6556 

558 

6634 

6712 

6790 

6868 

6945 

7023 

7101 

7x79 

7256 

7334 

N. 

0 

1 

2 

3 

4 

5 

i 

7 

8 

9 

D. 

86 

9 

-7 

26 

34 

43 

52 

60 

69 

77 

85  fi 

17 

26 

34 

43 

5i 

60 

68 

77 

n 

84  £ 

8 

25 

34 

42 

5o 

59 

67 

76 

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83  2 

8 

17 

25 

33 

42 

5o 

58 

6fr 

75 

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82  g, 
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8 

16 

25 

33 

4i 

49 

57 

66 

74 

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81  'S 

8 

1  16 

24 

32 

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49 

57 

65 

73 

Q 

80  | 

8 

16 

24 

32 

4o 

48 

56 

64 

72 

79  £ 

8 

16 

24 

32 

4o 

47 

55 

63 

71 

78  * 

8 

16 

23 

3i 

39 

47 

55 

62 

70 

LOGARITHMS    OF    J\UMBERS. 


13 


N. 

0 

1 

2 

3 

4     5 

6 

7 

8 

9 

D. 

559 

7474i2 

7489 

7567 

7645 

7722 

7800 

7878 

79.55 

8o33 

8110 

78 

56o 

8188 

8266 

8343 

8421 

8498 

8576 

8653 

873i 

8808 

8885 

77 

56i 

8963 

9o4o 

9118 

9i95 

9272 

935o 

9427 

95o4 

9582 

9659 

562 

9736 

98i4 

9891 

9968 

..45 

.123 

.200 

.277 

.354 

.43i 

563 

75o5o8 

o586 

o663 

o74o 

0817 

0894 

0971 

io48 

1125 

I2O2 

564 

I279 

i356 

i433 

i5io 

1587 

i664 

i74i 

1818 

1895 

I972 

565 

2048 

2125 

22O2 

2279 

2356 

2433 

25o9 

2586 

2663 

2740 

566 

2816 

2893 

2970 

3o47 

3i23 

3200 

3277 

3353 

343o 

35o6 

567 

3583 

366o 

3736 

38i3 

3889 

3966 

4042 

4n9 

4ig5 

4272 

\ 

$68 

4348 

4425 

45oi 

4578 

4654 

4?3o 

4807 

4883 

4960 

5o36 

76 

569 

5lI2 

5i89 

5265 

534: 

54i7 

5494 

5570 

5646 

5722 

5799 

570 

5875 

595i 

602-7 

6io3 

6180 

6256 

6332 

64o8 

6484 

656o 

57i 

6636 

67I2 

6788 

6864 

694o 

7016 

7092 

7168 

7244 

7320 

572 

7396 

7472 

7548 

•7624 

7700 

7775 

785i 

7927 

8oo3 

8079 

573 

8i55 

823o 

83o6 

8382 

8458 

8533 

86o9 

8685 

8761 

8836 

574 

89I2 

8988 

9o63 

9i39 

92l4 

929o 

9366 

944i 

95l7 

9592 

575 

9668 

9743 

98i9 

9894 

997° 

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.121 

.196 

.272 

•  347 

75 

576 

760422 

o498 

o573 

o649 

0724 

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IO25 

IIOI 

577 

n76 

I25l 

i326 

1402 

i477 

i552 

1627 

1702 

1778 

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578 

I928 

2OO3 

2O78 

2i53 

2228 

23o3 

2378 

2453 

2529 

2604 

5  79 

2679 

2754 

2829 

2904 

2978 

3o53 

3i28 

32o3 

3278 

3353 

58o 

3428 

35o3 

3578 

3653 

3727 

38o2 

3877 

3952 

4027 

4ioi 

58i 

4i76 

425i 

4326 

44oo 

4475 

455o 

4624 

4699 

4774 

4848 

582 

4923 

4998 

5o72 

5i47 

5221 

5296 

537o 

5445 

5520 

5594 

583 

5669 

5743 

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5966 

6o4i 

6n5 

6190 

6264 

6338 

74 

584 

64i3 

6487 

6562 

6636 

67io 

6785 

6859 

6933 

7007 

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585 

7i56 

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73o4 

7379 

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7527 

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7675 

7749 

7823 

586 

7898 

7972 

8o46 

8120 

8i94 

8268 

8342 

-84i6 

8490 

8564 

587 

8638 

8712 

8786 

8860 

8934 

9008 

9o82 

9i56 

9230 

93o3 

588 

9377 

945  1 

9525 

9599 

9673 

9746 

9820 

9894 

9968 

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589 

77on5 

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59o 

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0926 

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io73 

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59i 

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1661 

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1808 

1881 

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202% 

2  1  02 

2175 

2248 

73 

2322 

2395 

2468 

2542 

26i5 

2688 

2762 

2835 

2908 

2081 

593 

3o55 

3i28 

3201 

3274 

3348 

3421 

3494 

3567 

364o 

3713 

594 

3786 

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3933 

4oo6 

4o79 

4i52 

4225 

4298 

437i 

4444 

595 

45i7 

459o 

4663 

4736 

48o9 

4882 

4955 

5028 

5ioo 

5i73 

596 

5246 

53i9 

5392 

5465 

5538 

56io 

5683 

5756 

5829 

5902 

597 

5974 

6o47 

6120 

6i93 

6265 

6338 

64n 

6483 

6556 

6629 

598 

6701 

6774 

6846 

69i9 

6992 

7o64 

7i37 

7209 

7282 

7354 

599 

7427 

7499 

7572 

7644 

77i7 

7789 

7862 

7934 

8006 

8o79 

72 

600 

8i5i 

8224 

8296 

8368 

844  1 

85i3 

8585 

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873o 

8802 

.  601 

8874 

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9i63 

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2042 

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2186 

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606 

2473 

2544 

2616 

2688 

2759 

283i 

29O2 

2974 

3o46 

3n7 

6o7 

3i89 

3260 

3332 

34o3 

3475 

3546 

36i8 

3689 

376i 

3832 

71 

608 

39o4 

3975 

4o46 

4n8 

4i89 

4261 

4332 

44o3 

4475 

4546 

6o9 

46i7 

4689 

4760 

483i 

4902 

4974 

5o45 

5n6 

5187 

5259 

610 

533o 

54oi 

5472 

£543 

56i5 

5686 

5757 

5828 

5899 

5970 

611 

6o4i 

6112 

6i83 

6254 

6325 

6396 

6467 

6538 

6609 

6680 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

77  » 

8 

i5 

23 

3i 

39 

46 

54 

62 

69 

8 

76  } 

8 

i5 

23 

3o 

38 

46 

53 

61 

68 

75  £ 

8 

i5 

23 

3o 

38 

45 

53 

60 

68 

2  ' 

74  ^< 

7 

i5 

23 

3o 

37 

44 

52 

59 

67 

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73  g, 

7 

i5 

22 

29 

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44 

5i 

58 

66 

S 

72  2 

7 

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22 

29 

36 

43 

5o 

58 

65 

7I  PH 

7 

i4 

31 

28 

36 

43 

5o 

57 

64 

14 


LOGARITHMS    OF    LUMBERS. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

612 

786751 

6822 

6893  6964 

7o35 

7io6 

7i77 

•7248 

73i9 

739o 

71 

6i3 

7460 

753i 

•7602 

7673 

7744 

78i5 

7885 

7956 

802-7 

8o98 

6i4 

8168 

8239 

83io 

838i 

845i 

8522 

8593 

8663 

8734 

88o4 

6i5 

8875 

8946 

9016 

9o87 

9l57 

9228 

9299 

9369 

944o 

95io 

616 

958i 

965i 

9722 

9792 

9863 

9933 

...4 

..74 

•  i44 

.215 

70 

6i7 

790285 

o356 

O426 

0496 

0567 

06  3  7 

0707 

o778 

o848 

o9i8 

618 

o988 

1059 

1129 

1199 

1269 

i34o 

i4io 

i48o 

i55o 

1620 

6i9 

i69i 

i76i 

i83i 

1901 

1971 

2041 

2III 

2181 

2252 

2322 

620 

2392 

2462 

2532 

2602 

2672 

2742 

•>8l2 

2882 

2952 

3022 

621 

3o92 

3i62 

323i 

33oi 

337i 

344i 

35u 

358i 

365i 

372I 

622 

3790 

386o 

393o 

4ooo 

4o7o 

4i39 

4209 

4279 

4349 

44i8 

623 

4488 

4558 

4627 

4697 

4767 

4836 

49o6 

4976 

5o45 

5n5 

624 

5i85 

5254 

5324 

5393 

5463 

5532 

5602 

5672 

574i 

58n 

625 

588o 

5949 

6019 

6088 

6i58 

6227 

6297 

6366 

6436' 

v65o5 

69 

626 

6574 

6644 

67i3 

6782 

6852 

692I 

6990 

•7060 

7I29 

7i98 

627 

•7268 

7337 

74o6 

7475 

7545 

7614 

7683 

77'52 

-7821 

628 

796o 

8029 

8098 

8167 

8236 

83o5 

_83?4 

8443 

85i3 

8^82 

620, 

865i 

8720 

8-789 

8858 

8927 

8996 

9o65 

9i34 

9203 

9272 

63o 

934i 

9409 

9478 

9547 

9616 

9685 

9754 

9823 

9892 

996i 

63i 

8ooo29 

0098 

oi67 

0236 

o3o5 

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o5u 

o58o 

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632 

0717 

0-786 

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O923 

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1061 

II29 

n98 

1266 

i335 

633 

i4o4 

l472 

i54i 

1609 

i678 

i747 

i8i5 

1  88.; 

I952 

2021 

634 

2o89 

2i58 

2226 

2295 

2363 

2432 

25oo 

2568 

2637 

27o5 

635 

2774 

2842 

2910 

2979 

3o47 

3u6 

3i84 

3252 

332i 

3389 

68 

636 

3457 

3525 

3594 

3662 

373o 

3798 

3867 

3935 

4oo3 

4o7i 

637 

4i39 

4208 

4276 

4344 

44i2 

448o 

4548 

46i6 

4685 

4?53 

638 

4821 

4889 

4957 

5o25 

5o93 

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5229 

5297 

5365 

5433" 

639 

55oi 

5569 

5637 

57o5 

5773 

584i 

5908 

5976 

6o44 

6112 

64o 

6180 

6248 

63i6 

6384 

645  1 

65i9 

6587 

6655 

6723 

670.0 

64  1 

6858 

6926 

6994 

7061 

7I29 

7197 

7264 

7332 

74oo 

7467 

1  642 

7535 

76o3* 

767o 

7738 

•7806 

7873 

7941 

8008 

80-76 

8i43 

I  643 

8211 

82?9 

8346 

84i4 

848  1 

8549 

8616 

8684 

875i 

8818 

67 

644 

8886 

902I1 

9o88 

9i56 

9223 

9290 

9358 

9425 

9492 

645 

9f>6o 

962-7 

9694 

9762 

9829 

9896 

9964 

.  .3i 

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646 

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o3oo 

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o5oi 

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647 

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09-71 

io39 

1  1  06 

H73 

1240 

1307 

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i44i 

i5o8 

648 

i575 

1642 

I7o9 

1776 

i843 

I9IO 

1977 

2044 

2III 

2178 

649 

2245 

23l2 

2379 

2445 

25l2 

2579 

2646 

27l3 

2780 

2847 

65o 

29l3 

2980 

3o47 

3n4 

3i8i 

33i4 

338x 

3448 

35x4 

65i 

358i 

3648 

37i4 

378i 

3848 

39i4 

398i 

4o48 

4ii4 

4i8i 

652 

4248 

43i4 

438i 

4447 

45i4 

458  1 

4647 

47i4 

478o 

4847 

653 

49i3 

4980 

5o46 

5u3 

51-79 

5246 

53i2 

5378 

5445 

55n 

66 

654 

5578 

5644 

57i  i 

5777 

5843 

59io 

5976 

6042 

6io9 

6i75 

655 

6241 

63o8 

6374 

644o 

65o6 

6573 

6639 

67o5 

677i 

6838 

, 

656 

69o4 

69-70 

7o36 

7102 

•7169 

7235 

73oi 

7367 

7433 

7499 

657 

7565 

763i 

7698 

7764 

783o 

7896 

7962 

8028 

8o94 

8160 

658 

8226 

8292 

8358 

8424 

8490 

8556 

8622 

8688 

8754 

8820 

659 

8885 

895i 

9oi7 

9083 

9149 

92l5 

0281 

9346 

94l2 

9478 

660 
661 

9544 
820201 

96io 
026-7 

9676 
o333 

974i 
o399 

o464 

9873 
653o 

llll 

...4 
0661 

..70 

0727 

.i36 
0792 

662 

o858 

O924 

o989 

io55 

1120 

1186 

I25l 

i3i7 

1382 

i448 

663 

i5i4 

i579 

i645 

I7IO 

i775 

i84i 

I9o6 

I972 

2037 

2103 

65 

664 

2168 

2233 

2299 

2364 

243o 

2495 

256o 

2626 

269I 

2756 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

71  « 

7 

i4 

21 

28 

36 

43 

5o 

57 

64 

£ 

7o  £ 

7 

i4 

21 

28 

35 

42 

49 

56 

63 

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69  p. 

7 

i4 

21 

28 

35 

4i 

48 

55 

62 

£  * 

68  ..  . 

7 

i4 

20 

27 

34 

4i 

43 

54 

61 

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67  §. 

7 

i3 

30 

27 

34 

4o 

47 

54 

60 

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66  2 

7 

i3 

20 

26 

33 

4o 

46 

53 

59 

65  £< 

7 

i3 

20 

26 

33 

39 

46 

52 

59 

LOGARITHMS    OF    NUMBERS. 


N. 

0 

1 

2 

3 

4     5 

6 

7 

8 

9 

D. 

665 

822822 

2887 

2952 

3oi8 

3o83 

3i48 

32i3 

3279 

3344 

3409 

65 

666 

3474 

3539 

36o5 

3670 

3735 

38oo 

3865 

393o 

3996 

4o6i 

667 

4126 

4191 

4256 

4321 

4386 

445  1 

45i6 

458i 

4646 

4711 

668 

4776 

484i 

4go6 

4971 

5o36 

5ioi 

5i66 

523i 

5296 

536i 

669 

5426 

5491 

5556 

562i 

5686 

575i- 

58i5 

588o 

5945 

6010 

670 

6075 

6i4o 

6204 

6269 

6334 

6399 

6464 

6528 

6593 

6658 

671 

6723 

6787 

6852 

6917 

698i 

7046 

7111 

7i75 

•7240 

73o5 

672 

7369 

7434 

7499 

7563 

7628 

7692 

7757 

•7821 

7886 

795i 

673 

8oi5 

8o'8o 

8i44 

8209 

8273 

8338 

8402 

8467 

853i 

8595 

64 

674 

8660 

8724 

8789 

8853 

89i8 

8982 

9046 

9111 

9i75 

9239 

675 

93o4 

9368 

9432 

9497 

956i 

9625 

9690 

9754 

9818 

9882 

676 

9947 

.  .11 

..75 

.189 

.2O4 

.268 

.332 

.396 

.46o 

.525 

677 

83o589 

o653 

0717 

0781 

0845 

o9o9 

0973 

io37 

IIO2 

1166 

678 

1230 

1294 

i358 

1422 

i486 

i55o 

1614 

i678 

1742 

1806 

679 

1870 

1934 

1998 

2062 

2126 

2189 

2253 

23l7 

23~8i 

2445 

680 

2509 

2573 

2637 

2700 

2764 

2828 

2892 

2956 

3020 

3o83 

68  1 

3i47 

3211 

3275 

3338 

3402 

3466 

353o 

SSgS 

3657 

3721 

682 

3784 

3848 

3912 

3975 

4o39 

4io3 

4i66 

4*3o 

4294 

4357 

683 

442i 

4484 

4548 

46n 

4675 

4739 

4802 

4866 

4929 

4993 

684 

5o56 

5l20 

5i83 

5247 

53io 

5373 

5437 

55oo 

5564 

5627 

63 

685 

6691 

5754 

58i7 

588i 

5944 

6007 

6071 

6r34 

619-7 

-6261 

686 

6324 

6387 

645  1 

65i4 

6577 

664i 

6704 

6767 

683o 

6894 

687 

6957 

7020 

7o83 

7i46 

•7210 

7273 

7336 

7399 

7462 

7525 

688 

7588 

7652 

771.5 

7778 

784i 

7904 

7967 

8o3o 

8093 

8i56 

689 

8219 

8282 

8345 

84o8 

847i 

8534 

8597 

8660 

87a3 

8786 

690 

8849 

8912 

8975 

9o38 

9ioi 

9164 

9227 

9289 

9352 

94i5 

691 

9478 

954i 

96o4 

9667 

9729 

9792 

9855 

9918 

998i 

..43 

692 

84oio6 

0169 

0232 

0294 

o357 

O420 

0482 

o545 

0608 

0671 

693 

0733 

o796 

o859 

092I 

0984 

io46 

1109 

1172 

1234 

I297 

694 

1359 

l422 

i485 

1  547 

1610 

1672 

I735 

1797 

1860 

I922 

695 

1985 

2047 

2IIO 

2172 

2235 

2297 

236o 

2422 

2484 

2547 

6a 

696 

2609 

2672 

2734 

2796 

2859 

2921 

2983 

3o46 

3io8 

3170 

697 

3233 

3295 

3357 

3420 

3482 

3544 

36o6 

3669 

373i 

3793 

698 

3855 

3918 

398o 

4042 

4io4 

4i66 

4229 

4291 

4353 

44i5 

699 

4477 

4539 

46oi 

4664 

4-726 

4788 

485o 

4912 

4974 

5o36 

700 

5098 

5i6o 

5222 

5284 

5346 

54o8 

5470 

5532 

5594 

5656 

701 

57i8 

578o 

5842 

59o4 

5966 

6028 

6090 

6i5i 

6213 

6275 

702 

6337 

6399 

646  1 

6523 

6585 

6646 

6708 

6770 

6832 

6894 

7o3 

6955 

7oi7 

7079 

7141 

7202 

7264 

7326 

7388 

7449 

75n 

704 

7573 

7634 

7696 

7758 

7819 

7881 

7943 

8oo4 

8066 

8128 

705 

8189 

825i 

83i2 

8374 

8435 

8497 

8559 

8620 

8682 

8743 

706 

88o5 

8866 

8928 

8989 

9o5i 

9112 

9i74 

9235 

9297 

^358 

61 

707 

9419 

948i 

9542 

96o4 

9665 

9726 

9788 

9849 

9911 

9972 

708 

85oo33 

0095 

oi56 

0217 

0279 

o34o 

o4oi 

0462 

o524 

o585 

709 

o646 

070? 

0769 

o83o 

0891 

0952 

1014 

io75 

n36 

n97 

710 

1258 

1320 

i38i 

1442 

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i564 

1625 

1686 

1747 

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711 

1870 

1931 

1992 

2o53 

2Il4 

2175 

2236 

2297 

2358 

24l9 

712 

2480 

254i 

2602 

2663 

2724 

2785 

2846 

2907 

2968 

3o29 

718 

Sogo 

3i5o 

3211 

3272 

3333 

3394 

3455 

35i6 

35?7 

3637 

7i4 

3698 

3759 

3820 

388i 

394i 

4002 

4o63 

4124 

4i85 

4245 

7i5 

43o6 

4367 

4428 

4488 

4549 

46io 

467o 

473i 

4792 

4852 

716 

4gi3 

49?4 

5o34 

5o95 

5i56 

52i6 

52?7 

5337 

5398 

5459 

717 

55i9 

558o 

564o 

5701 

5761 

5822 

5882 

5943 

6oo3 

6o64 

718 

6124 

6i85 

6245 

63o6 

6366 

6427 

6487 

6548 

6608 

6668 

60 

719 

6729 

6789 

685o 

69io 

697° 

7o3i 

7o9i 

7l52 

7212 

7272 

N. 

0 

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2 

3 

4   ||  5 

6 

7 

8 

9 

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64  og 

6 

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26 

32 

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45 

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58 

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6 

12 

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43 

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56 

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12 

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43 

49 

55 

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6 

12 

18 

24 

3o 

36 

42 

48 

54 

LOGARITHMS    OF   NUMBERS. 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

720 

857332 

7393 

7453 

75i3 

7b74 

7634  7694 

7755 

78i5 

7875 

60 

721 

7935 

7995 

8o56 

8116 

8i76 

8236 

8297 

8357 

84i7 

8477 

722 

8537 

8597 

8657 

87i8 

8778 

8838 

8898 

8958 

9oi8 

9o78 

723 

9i38 

9198 

9258 

9318 

9379 

9439 

9499 

9559 

96i9 

9679 

724 

9739 

9799 

9859 

99i8 

997s 

..38 

..98 

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726 

86o338 

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o697 

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726 

o937 

0996 

io56 

1116 

H76 

1236 

1295 

i355 

i4i5 

i475 

727 

i534 

1594 

i654 

1-714 

I773 

i833 

i893 

I952 

2012 

2O72 

728 

2l3l 

2191 

225l 

23lO 

2370 

243o 

2489 

2549 

2608 

2668 

729 

2-728 

2787 

2847 

29o6 

2966 

3o25 

3o85 

3i44 

3-204 

3263 

73o 

3323 

3382 

3442 

35oi 

356i 

3620 

368o 

3739 

3799 

3858 

59 

73i 

39i7 

3977 

4o36 

4o96 

4i55 

42i4 

4274 

4333 

4392 

4452 

732 

45n 

457o 

463o 

4689 

4748 

48o8 

4867 

4926 

4985 

5o45 

733 

5io4 

5i63 

5222 

5282 

534i 

54oo 

5459 

55i9 

5578 

5637 

734 

5696 

5755 

58i4 

5874 

5933 

5992 

6o5i 

6110 

6i69 

6228 

735 

6287 

6346 

64o5 

6465 

6524 

6583 

6642 

6701 

676o 

68i9 

736 

68  78 

6937 

6996 

7o55 

7n4 

7i73 

7232 

729i 

735o 

74o9 

737 

7467 

7526 

7585 

7644 

77o3 

7762 

782I 

7880 

7939 

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738 

8o56 

8n5 

8i74 

8233 

8292 

835o 

8409 

8468 

852? 

8586 

739 

8644 

87o3 

8762 

8821 

8879 

8938 

8997 

9o56 

9ii4 

9i73 

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9232 

9290 

9349 

94o8 

9466 

9525 

9584 

9642 

97oi 

976o 

74i 

9818 

9877 

9935 

9994 

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.1-70 

.228 

.28-7 

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742 

87o4o4 

0462 

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08-72 

0930 

58 

743 

0989 

1047 

1106 

n64 

1223 

1281 

1339 

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i5i5 

744 

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1690 

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1806 

1  865 

1923 

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2040 

2098 

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2i56 

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2273 

233i 

2389 

2448 

25o6 

2564 

2622 

2681 

746 

2739 

2797 

2855 

2913 

2972 

3o3o 

3o88 

3i46 

3204 

3262 

747 

332i 

3379 

3437 

3495 

3553 

36ii 

3669 

3727 

3785 

3844 

748 

3902 

3960 

4oi8 

4o76 

4i34 

4192 

425o 

43o8 

4366 

4424 

7^9 

4482 

4540 

4598 

4656 

47i4 

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483o 

4888 

4945 

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75o 

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5119 

5i77 

5235 

5293 

535i 

54o9 

5466 

5524 

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75i 

564o 

5698 

5756 

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5929 

5987 

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6102 

6160 

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6218 

62-76 

6333 

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6449 

65o7 

6564 

6622 

6680 

6737 

753 

6795 

6853 

69io 

6968 

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7083 

7i4i 

7i99 

7256 

73i4 

754 

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7429 

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7832 

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7947 

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8062 

8119 

8177 

8234 

8292 

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57 

756 

8522 

8579 

8637 

8694 

8752 

8809 

8866 

8924 

898i 

9o39 

757 

9096 

9i53 

92II 

9268 

9325 

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9555 

9612 

758 

9669 

9726 

9784 

984i 

9898 

9956 

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759 

880242 

0299 

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08-71 

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I27I 

i328 

761 

1  385 

1  442 

1499 

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1784 

1841 

1898 

762 

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2OI2 

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2i83 

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229-7 

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763 

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2923 

298o 

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32O7 

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3377 

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4909 

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553i 

5587 

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769 

5926 

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6a65 

632i 

6378 

6434 

56 

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7336 

7392 

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772 

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7674 

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7786 

7842 

7898 

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8292 

8348 

84o4 

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85i6 

8573 

8629 

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9°77 

9i34 

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9246 

N.    0    1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

60  a 

6 

12 

18 

24 

3o 

36 

42 

48 

54 

£ 

59  S 

6 

12 

18 

24 

3o 

35 

4i 

47 

53 

| 

58  PH  . 

6 

12 

17 

23 

29 

35 

4i 

46 

52 

ft 

57  o 

6 

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J7 

23 

29 

34 

4o 

46 

5i 

56  £ 

6 

II 

17 

23 

28 

34 

39 

45 

5o 

• 

LOGARITHMS    OF    NUMBERS. 


17 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

7?5 

889302 

9358 

94i4 

947o 

9526 

9582 

9638 

9694 

975o 

98o6 

56 

776 

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9918 

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111 

890421 

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0812 

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1091 

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1203 

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i3i4 

i37o 

1426 

1482 

779 

i537 

i593 

1649 

1705 

I76o 

1816 

l872 

I928 

I983 

2o39 

780 

2096 

2i5o 

2206 

2262 

23l7 

2373 

2429 

2484 

254o 

2595 

781 

2661 

2707 

2762 

2818 

2873 

2929 

2985 

3o4o 

3o96 

3i5i 

782 

3207 

3262 

33i8 

3373 

3429 

3484 

354o 

3595 

365i 

37o6 

783 

3762 

38i7 

3873 

3928 

3984 

4o39 

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4i5o 

42o5 

4261 

55 

784 

43i6 

437i 

4427 

4482 

4538 

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4648 

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48i4 

785 

4870 

4925 

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5o36 

5o9i 

5i46 

5201 

5257 

53i2 

5367 

786 

5423 

5478 

5533 

5588 

5644 

5699 

5754 

58o9 

5864 

5920 

787 

5975 

6o3o 

6o85 

6i4o 

6i95 

625i 

63o6 

636i 

64i6 

647i 

788 

6626 

658i 

6636 

6692 

6747 

6802 

6857 

69I2 

6967 

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789 

7077 

7l32 

7187 

7242 

7297 

7352 

74o7 

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7572 

79° 

7627 

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7737 

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7957 

8012 

8o67 

8122 

791 

8176 

823i 

8286 

834i 

8396 

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867o 

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8835 

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8944 

8999 

9o54 

9io9 

9i64 

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793 

0273 

9828 

9383 

9437 

9492 

9547 

9602 

9656 

9711 

9766 

794 

9821 

9875 

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9985 

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.258 

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795 

900367 

0422 

0476 

o53i 

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796 

0913 

0968 

1022 

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1186 

1240 

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i5i3 

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1622 

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I73i 

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i84o 

i894 

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54 

798 

2003 

2057 

2112 

2166 

2221 

2275 

2329 

2384 

2438 

2492 

799 

2647 

2601 

2655 

2710 

2764 

28l8 

2873 

2927 

2981 

3o36 

800 

3090 

3i44 

3i99 

3253 

33o7 

336i 

34i6 

3470 

3524 

35.78 

801 

3633 

3687 

374i 

3795 

3849 

3904 

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4229 

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4824 

4878 

4932 

4986 

5o4o 

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52O2 

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6266 

53io 

5364 

54i8 

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5526 

558o 

5634 

5688 

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6796 

585o 

59o4 

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6012 

6066 

6119 

6173 

6227 

6281 

806 

6335 

6389 

6443 

6497 

655i 

6604 

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6712 

6766 

6820 

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6874 

6927 

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784i 

7895 

809 

7949 

8002 

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8110 

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8270 

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810 

8485 

8539 

8592 

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88o7 

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9021 

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9128 

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9342 

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0731 

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1264 

1317 

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1477 

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1  584 

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1690 

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1797 

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1956 

2OO9 

2o63 

2116 

2l69 

817 

2222 

2275 

2328 

238i 

2435 

2488 

254l 

2594 

2647 

27OO 

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2753 

2806 

2859 

2913 

2966 

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3i78 

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819 

3284 

3337 

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3443 

3496 

3549 

36o2 

3655 

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376i 

820 

38i4 

3867 

3920 

3973 

4026 

4o79 

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4237 

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821 

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4396 

4449 

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466o 

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4766 

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822 

4872 

4925 

4977 

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5o83 

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524i 

5294 

5347 

828 

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5927 

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6i38 

6191 

6243 

6296 

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64oi 

826 

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6559 

6612 

6664 

67i7 

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6822 

6875 

6927 

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7243 

7295 

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827 

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7558 

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7663 

77i6 

7768 

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7873 

7925 

7978 

52 

828 

8o3o 

8o83 

8i35 

8188 

8240 

8293 

8345 

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845o 

85o2 

829 

8555 

8607 

8659 

87I2 

8764 

8816 

8869 

892I 

8973 

9O26 

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9078 

9i3o 

9183 

9235 

9287 

9340 

9392 

9444 

9496 

9549 

N,  |   0   |  1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

.  f  55  o5  f  6 

ii 

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22 

28 

33 

39 

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ii 

16 

22 

27 

32 

38 

43 

49 

5   53  P;j   5 

ii 

16 

21 

27 

32 

37 

42 

48 

Q  I  62  £  I  5 

10 

16 

21 

26 

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36 

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B 


18 


LOGARITHMS    OF    NUMB 


E  RS. 


N. 

VI  i 

2 

3 

4     5 

6 

7 

8 

9 

D. 

83i 

919601  (  g653  9706 

9758 

98io 

9862 

99*4 

9967 

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52 

832 

920123 

0176 

0228 

0280 

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o436 

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o54i 

o593 

833 

o645 

0697 

0749 

0801 

o853 

0906 

o958 

IOIO 

1062 

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834 

ii  66 

I2i8 

1270 

l322 

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1426 

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i53o 

i582 

1  634 

835 

1686 

1733 

1790 

1842 

i894 

I946 

i998 

2o5o 

2IO2 

2i54 

836 

2206 

2258 

s3io 

2362 

24i4 

2466 

25i8 

2570 

2622 

2674 

837 

2725 

2777 

2829 

2881 

2933 

2985 

3o37 

3o89 

3i4o 

3i92 

838 

3244 

3296 

3348 

3399 

345  1 

35o3 

3555 

36o7 

3658 

3710 

839 

3762 

38i4 

3865 

39i7 

3969 

4021 

4o72 

4i2A 

4176 

4228 

84o 

4279 

433i 

4383 

4434 

4486 

4538 

4589 

464? 

4693 

4744 

84i 

4796 

4848 

4899 

495i 

5oo3 

5o54 

5io6 

5i57 

52O9 

5261 

842 

53i2 

5364 

54i5 

5467 

55i8 

557o 

562i 

5673 

5725 

5776 

843 

5828 

5879 

593i 

5982 

6o34 

6o85 

6i37 

6188 

6240 

629I 

5i 

844 

6342 

6394 

6445 

6497 

6548 

6600 

665i 

6702 

6754 

68o5 

845 

6857 

6908 

6959 

7OII 

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7n4 

7i65 

7216 

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73i9 

846 

737° 

7422 

7473 

7524 

7576 

7627 

7678 

773o 

778i 

7832 

84? 

7883 

7935 

7986 

8o37 

8088 

8i4o 

8191 

824« 

8293 

8345 

848 

8396 

8447 

8498 

8549 

8601 

8652 

87o3 

8754 

88o5 

8857 

849 

8908 

8959 

9010 

9o6i 

9I  12  1 

9163 

92l5 

9266 

93l7 

9368 

85o 

9419 

947° 

952I 

9572 

9623 

9674 

97s5 

9776 

9827 

9879 

85i 

993o 

998i 

..32 

..83 

.134 

.i85 

.236 

.287 

.338 

.389 

852 

93o44o 

o49i 

o542 

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o643 

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853 

0949 

IOOO 

io5i 

1102 

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I2O4 

1254 

i3o5 

i356 

1407 

854 

i458 

i5o9 

i56o 

1610 

166! 

I7I2 

1763 

1814 

i865 

I9i5 

855 

1966 

2017 

2068 

2118 

2i69 

222O 

2271 

2322 

2372 

2423 

856 

2474 

2524 

2575 

2626 

2677 

2727 

2778 

2829 

a879 

293o 

857 

2981 

3o3i 

3o82 

3i33 

3i83 

3234 

3285 

3335 

3386 

3437 

858 

3487 

3538 

3589 

3639 

369o 

374o 

379i 

384i 

3892 

3943 

859 

3993 

4o44 

4094 

4i45 

4i95 

4246 

4296 

4347 

4397 

4448 

860 

4498 

4549 

4599 

465o 

4700 

475i 

48oi 

4852 

4902 

4953 

5o 

86  1 

5oo3 

5o54 

5io4 

5i54 

52o5 

5255 

53o6 

5356 

5406 

5457 

862 

55o7 

5558 

56o8 

5658 

5709 

5759 

58o9 

586o 

59io 

596o 

i 

863 

6011 

6061 

6m 

6162 

6212 

6262 

63i3 

6363 

64i3 

6463 

864 

65i4 

6564 

66i4 

6665 

67i5 

6765 

68i5 

6865 

69i6 

6966 

865 

7016 

7066 

7117 

7i67 

7217 

7267 

73i7 

7367 

74i8 

7468 

866 

75i8 

75B8 

7618 

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7718 

7769 

7819 

7869 

79i9 

7969 

867 

8019 

8069 

8119 

8i69 

8219 

8269 

8320 

8^0 

8420 

847o 

868 

8520 

857o 

8620 

867o 

8720 

877o 

8820 

887o 

8920 

897o 

869 

9020 

9070 

9120 

9i7o 

9220 

9270 

9320 

9369 

94i9 

9469 

870 

95i9 

9569 

9619 

9669 

9719 

9769 

98i9 

9869 

99i8 

9968 

871 

94ooi8 

0068 

0118 

0168 

0218 

0267 

o3i7 

o367 

o4i7 

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872 

o5i6 

o566 

0616 

0666 

0716 

o765 

o8i5 

o865 

o9i5 

o964 

873 

1014 

io64 

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n63 

I2l3 

1263 

i3i3 

i362 

1412 

1462 

874 

i5n 

1661 

1611 

1660 

1710 

I76o 

i8o9 

i859 

I909 

i958 

875 

2008 

2o58 

2107 

2l57 

2207 

2256 

23o6 

2355 

24o5 

2455 

876 

25o4 

2554 

26o3 

2653 

2702 

2752 

2801 

285i 

29OI 

295o 

877 

3ooo 

3o4g 

3o99 

3i48 

3i98 

3247 

3297 

3346 

3396 

3445 

49 

878 

3495 

3544 

3593 

3643 

3692 

374a 

379i 

384i 

389o 

3939 

879 

3989 

4o38 

4o88 

4i37 

4i86 

4236 

4285 

4335 

4384 

4433 

880 

4483 

4532 

458i 

463i 

468o 

4729 

4779 

4828 

4877 

4927 

Hi 

4976 

5o25 

5074 

5i24 

5i73 

5222 

5272 

532i 

537o 

54i9 

882 

5469 

55i8 

5567 

56i6 

5665 

57i5 

5764 

58i3 

5862 

59I2 

883 

596i 

6010 

6059 

6108 

6157 

62O7 

6256 

63o5 

6354 

64o3 

884 

6452 

65oi 

655i 

6600 

6649 

6698 

6747 

6796 

6845 

6894 

885 

6943 

6992 

704  1 

7o9o 

7140 

7i89 

7238 

•728-7 

7336 

7385 

886 

7434 

7483 

7532 

758i 

763o 

7679 

7728 

7777 

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7875 

N.    0   |  1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

.  f  52  a  f  5 

10 

16 

21 

26 

3i 

36 

42 

47 

fe   5i  SI  5 

10 

16 

2O 

26 

3i 

36 

4i 

46 

fe   5o  M   S 

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20 

25 

3o 

35 

4o 

45 

q  I  49  *  {  5 

10 

i5 

2O 

25 

29 

34 

39 

44 

LOGARITHMS    OF    NUMBERS. 


N. 

0 

1 

2 

3 

4  |  5 

6 

7 

8 

9 

D. 

887 

947924 

7978 

8022 

8070 

8lI9 

8168 

8217 

8266 

83i5 

8364 

49 

888 

84i3 

8462 

85u 

856o 

8609 

8657 

8706 

8755 

88o4 

8853 

889 

8902 

895i 

8999 

9048 

9°97 

9i46 

9i95 

9244 

9292 

934i 

890 

9890 

9489 

9488 

9536 

9585 

9634 

9688 

9781 

9780 

9829 

891 

9878 

9926 

9975 

..24 

..78 

.121 

.  170 

.219 

.267 

.816 

892 

95o365 

o4i4 

0462 

o5n 

o56o 

0608 

0657 

0706 

o754 

0808 

893 

0861 

0900 

0949 

0997 

io46 

lOgS 

u43 

1192 

1240 

1289 

894 

1888 

1886 

i435 

i483 

i532 

i58o 

1629 

1677 

1726 

i775 

895 

1828 

1872 

1920 

1969 

2017 

2066 

2Il4 

2168 

2211 

2260 

48 

896 

2808 

2356 

24o5 

2453 

2502 

255o 

2599 

2647 

2696 

2744 

897 

2792 

2841 

2889 

2988 

2986 

3o34 

3o83 

8181 

3i8o 

8228 

898 

8276 

3325 

3373 

3421 

3470 

35i8 

3566 

36i5 

3663 

37n 

899 

8760 

8808 

3856 

8905 

3953 

4ooi 

4o4g 

4o98 

4i46 

4i94 

900 

4243 

4291 

4339 

4387 

4435 

4484 

4532 

458o 

4628 

4677 

901 

4726 

4??3 

4821 

4869 

4918 

4966 

5oi4 

5o62 

5no 

5i58 

902 

6207 

5255 

53o3 

535i 

5399 

5447 

5495 

5543 

5592 

564o 

908 

5688 

5736 

5784 

5832 

588o 

5928 

5976 

6024 

6072 

6120 

904 

6168 

6216 

6265 

6818 

636i 

6409 

6457 

65o5 

6553 

6601 

906 

6649 

6697 

6745 

6793 

684o 

6888 

6986 

6984 

7082 

•7080 

906 

7128 

7176 

7224 

7272 

7820 

7368 

7416 

7464 

7512 

7559 

997 

7607 

7655 

7708 

775  1 

7799 

7847 

7894 

7942 

799° 

8088 

908 

8086 

8i34 

8181 

8229 

8277 

8325 

8878 

8421 

8468 

85i6 

909 

8564 

8612 

8659 

8707 

8755 

8808 

885o 

8898 

8946 

8994 

910 

9041 

9089 

9i37 

9i85 

9232 

928o 

9828 

9375 

9423 

9471 

911 

95i8 

9566 

9614 

9661 

-97°9 

9757 

9804 

9852 

99°° 

9947 

912 

9995 

..42 

..90 

.188 

.i85 

.288 

.280 

.828 

.876 

.428 

9i3 

960471 

o5i8 

o566 

o6i3 

0661 

0709 

0756 

0804 

o85i 

0899 

914 

0946 

0994 

io4i 

1089 

n36 

n84 

1281 

1279 

1826 

i374 

47 

916 

1421 

1469 

i5i6 

i563 

1611 

i658 

1706 

i753 

1801 

1  848 

916 

i895 

1943 

1990 

2088 

2o85 

2182 

2180 

2227 

2275 

2822 

917 

2869 

2417 

2464 

25ll 

2559 

2606 

2653 

2701 

2748 

2795 

918 

2843 

2800 

2937 

2985 

'8082 

8079 

8126 

8174 

8221 

8268 

919 

33i6 

3363 

34io 

3457 

35o4 

3552 

3599 

3646 

3693 

374i 

920 

8788 

3835 

8882 

8929 

8977 

4024 

4071 

4n8 

4i65 

4212 

921 

4a6o 

43o7 

4354 

44oi 

4448 

4495 

4542 

4590 

4637 

4684 

922 

4?3i 

4778 

4825 

4872 

4919 

4966 

5oi3 

5o6i 

5io8 

5i55 

928 

6202 

5249 

5296 

5343 

5390 

5437 

5484 

553i 

5578 

5625 

924 

5672 

5719 

5766 

58i3 

586o 

59o7 

5954 

6001 

6o48 

6oo5 

925 

6142 

6189 

6286 

6288 

6829 

6376 

64s3 

6470 

65  1  7 

6564 

926 

66u 

6658 

6705 

6752 

6799 

6845 

6892 

6989 

6986 

7o33 

927 

7080 

7127 

7i73 

7220 

7267 

73i4 

736i 

7408 

7454 

75oi 

928 

7548 

7595 

7642 

7688 

7735 

7782 

7820. 

7875 

7922 

7969 

929 

8016 

8062 

8109 

8i56 

8208 

8249 

8296 

8343 

8890 

8436 

980 

8483 

853o 

8576 

8628 

8670 

8716 

8768 

8810 

8856 

8908 

93! 

895o 

8996 

9o43 

9090 

9186 

9i83 

9229 

9276 

9828 

9869 

982 

9416 

9463 

95o9 

9556 

9602 

9649 

9695 

9742 

9789 

9835 

988 

9882 

9928 

9975 

.  .21 

..68 

.n4 

.161 

.207 

.254 

.800 

934 

970347 

0893 

o44o 

o486 

o533 

o579 

0626 

0672 

0719 

0765 

46 

935 

0812 

o858 

0904 

ogSi 

0997 

io44 

io9o 

1187 

1188 

1229 

986 

1276 

1822 

1869 

i4i5 

i46i 

i5o8 

i554 

1601 

1  647 

1698 

987 

1740 

1786 

i832 

1879 

1925 

1971 

2018 

2064 

2110 

2157 

988 

2^208 

2249 

2295 

2842 

2888 

2434 

2481 

2527 

2573 

2619 

989 

21666 

2712 

2758 

2804 

285i 

2897 

2943 

2989 

3o35 

8082 

940 

8128 

3i74 

8220 

8266 

33i3 

SSSg 

34o5 

345  1 

3497 

3543 

94  1 

359o 

3636 

3682 

8728 

3774 

8820 

3866 

8918 

3959 

4oo5 

942 

4o5i 

4097 

4i43 

4i89 

4235 

4281 

4827 

4374 

4420 

4466 

943 

45i2 

4558 

46o4 

465o 

4696 

4742 

4788 

4834 

488o 

4926 

N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

u 

48  »  f  5 

10 

i4 

19  . 

24 

29 

34 

38 

43 

§. 

47  M  5 

9   i4 

*9 

24 

28 

33 

38 

42 

. 

46  *  I  5 

9   r4 

18 

28 

28 

32 

37 

4i 

LOGARITHMS    OF    NUMBERS. 


N. 

0 

1 

2 

3    4     5 

6 

7 

8 

9 

D. 

944 

974972 

6018 

5o64 

5no 

5i56 

52O2 

5248 

5294 

534o 

5386 

46 

945 

5432 

5478 

5524 

557o 

56i6 

5662 

57o7 

5753 

5799 

5845 

946 

589i 

5937 

5983 

6029 

6o75 

6121 

6i67 

6212 

6258 

63o4 

94? 

635o 

6396 

6442 

6488 

6533 

6579 

6625 

6671 

6717 

6763 

948 

6808 

6854 

6900 

6946 

6992 

7°37 

7o83 

7I29 

7i75 

722O 

949 

7266 

7312 

7358 

74o3 

7449 

7495 

754i 

7586 

7632 

7678 

95o 

7724 

7769 

78i5 

7861 

7906 

7952 

799s 

8o43 

8o89 

8i35 

95i 

8181 

8226 

8272 

8317 

8363 

84o9 

8454 

85oo 

8546 

859i 

o5'2 

8637 

8683 

8728 

8774 

8810 

8865 

89n 

8956 

9OO2 

9o47 

953 

9o93 

9i38 

9184 

923o 

9275 

932I 

9366 

94i2 

9457 

95o3 

954 

9548 

9^94 

9639 

9685 

973o 

9776 

982I 

9867 

99I2 

9958 

955 

98ooo3 

oo49 

oo94 

oi4o 

oi85 

023l 

0276 

0322 

o367 

O4l2 

45 

966 

o458 

o5o3 

o549 

o594 

o64o 

o685 

o73o 

o776 

0821 

o867 

967 

O9I2 

°957 

ioo3 

1048 

io93 

n39 

n84 

I229 

I275 

1320 

968 

i366 

i4n 

i456 

i5oi 

i547 

l592 

i637 

i683 

I728 

i773 

959 

i8i9 

1  864 

i9o9 

i954 

20OO 

2o45 

2090 

2i35 

2181 

2226 

960 

2271 

23i6 

2362 

2407 

2452 

2497 

2543 

2588 

2633 

2678 

961 

2723 

2769 

2814 

2859 

2904 

2949 

2994 

3o4o 

3o85 

3i3o 

962 

3175 

3220 

3265 

33io 

3356 

34oi 

3446 

349i 

3536 

358i 

963 

3626 

367i 

37i6 

3762 

38o7 

3852 

3897 

3942 

3987 

4o32 

964 

4077 

4l22 

4i67 

4212 

4257 

4302 

4347 

4392 

4437 

4482 

965 

4627 

4572 

46i7 

4662 

47o7 

4752 

4797 

4842 

4887 

4932 

966 

4977 

5022 

5o67 

5lI2 

5i57 

52O2 

5247 

5292 

5337 

5382 

967 

5426 

9*71 

55i6 

556i 

56o6 

565i 

5696 

574i 

5786 

583o 

968 

6876 

592O 

5965 

6010 

6o55 

6100 

6:44 

6i89 

6234 

6279 

969 

6324 

6369 

64i3 

6458 

65o3 

6548 

6593 

6637 

6682 

6727 

97° 

6772 

6817 

6861 

69o6 

695i 

6996 

7o4o 

7o85 

7i3o 

7i75 

971 

72I9 

7264 

73o9 

7353 

7398 

7443 

7488 

7532 

7577 

•7622 

972 

7666 

7711 

7756 

7800 

7845 

789o 

7934 

7979 

8024 

8068 

973 

8n3 

8i57 

8202 

8247 

8291 

8336 

838i 

8425 

847o 

85i4 

974 

8559 

86o4 

8648 

8693 

8737 

878,2 

8826 

8871 

89i6 

896o 

976 

9oo5 

9o49 

9o94 

9i38 

9i83 

9227 

9272 

93i6 

936i 

94o5 

976 

945o 

9494 

9539 

9583 

9628 

9672 

9717 

976i 

98o6 

985o 

44 

977 

9895 

9939 

9983 

..28 

..72 

.II7 

.161 

.206 

.250 

.294 

978 

99o339 

o383 

0428 

0472 

o5i6 

o56i 

o6o5 

o65o 

o694 

o738 

979 

o783 

0827 

o87i 

o9i6 

o96o 

ioo4 

1049 

io93 

n37 

1182 

980 

1226 

1270 

i3i5 

i359 

i4o3 

1  448 

l492 

i536 

i58o 

i625 

981 

i669 

I7i3 

i758 

1802 

1  846 

i89o 

i935 

i979 

2023 

2O67 

982 

2III 

2i56 

2200 

2244 

2288 

2333 

2377 

2421 

2465 

25o9 

983 

2554 

2598 

2642 

2686 

273o 

2774 

28l9 

2863 

2907 

295i 

984 

2995 

3o39 

3o83 

3l27 

3l72 

32i6 

3260 

33o4 

3348 

3392 

986 

3436 

348o 

3524 

3568 

36r3 

3657 

3701 

3745 

3789 

3833 

986 

3877 

392I 

3965 

4oo9 

4o53 

4o97 

4i4i 

4i85 

4229 

4273 

987 

43i7 

436i 

44o5 

4449 

4493 

4537 

458i 

4625 

4669 

47i3 

988 

4757 

48oi 

4845 

4889 

4933 

4977 

5021 

5o65 

5io8 

5i52 

989 

5i96 

524o 

5284 

5328 

5372 

54i6 

546o 

55o4 

5547 

559i 

99° 

5635 

5679 

5723 

5767 

58n 

5854 

5898 

594a 

5986 

6o3o 

991 

6074 

6117 

6161 

62o5 

6249 

6293 

6337 

638o 

6424 

6468 

992 

65i2 

6555 

6599 

6643 

6687 

6731 

6774 

6818 

6862 

69o6 

993 

6949 

6993 

7o37 

•7080 

•7124 

7168 

7212 

7255 

7299 

7343 

994 

7386 

743o 

7474 

75i7 

756i 

76o5 

7648 

7692 

7736 

7779 

995 

7823 

7867 

79io 

7954 

7998 

8o4i 

8o85 

8l29 

8l72 

8216 

996 

8259 

83o3 

8347 

839o 

8434 

8477 

852i 

8564 

8608 

8652 

997 

8695 

8739 

8782 

8826 

8869 

89i3 

8956 

9ooo 

9043 

9o87 

998 

9i3i 

9i74 

92l8 

9261 

93o5 

9348 

9392 

9435 

9479 

9522 

999 

9565 

9609 

9652 

9696 

9739 

9783 

9826 

9870 

99i3 

9957 

43 

N. 

0   |  1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

.  f  46  *  f  5 

9 

i4 

18 

23 

28 

32 

37 

4i 

JS  j  45  Si   5 

9 

i4 

18 

23 

27 

32 

36 

4i 

»  I  44-  «•  1  4 

9 

i3 

18 

22 

26 

3i 

35 

4o 

p  I  43  £  {  4 

9 

i3 

i? 

22 

26 

3o 

34 

39 

TABLE 


OF 


LOGARITHMIC  SINES  AID  TANGENTS 


FOR    EVERY 


TEN  SECONDS  OF  THE  QUADRANT. 


LOGARITHMIC    SINES. 


Min. 

Sine  of  0  Degree. 

P.  P«rt 

0" 

10" 

20" 

30" 

40" 

50" 

to  1". 

0 

Inf.  Neg. 

5.685575 

5.9866o5 

6.162696 

6.287635 

6.384545 

59 

1 

6.463726 

6.53o673 

6.588665 

639817 

685575 

726968 

58 

2 

764756 

799518 

83i7o3 

861666 

889695 

916024 

57 

3 

940847 

964328 

9866o5 

7.007794 

7.027997 

7-o473o3 

56 

4 

7.065786 

7.o835i5 

7.ioo548 

116939 

i32733 

i47973 

55 

5 

162696 

176936 

190725 

204089 

217054 

229643 

54 

6 

241877 

253776 

265358 

276639 

287635 

298358 

53 

7 

3o8824 

319043 

329027 

338787 

348332 

357672 

52 

8 

3668r6 

37577i 

384544 

393i45 

401578 

409850 

5i 

9 

417968 

425937 

433762 

44i449 

449002 

456426 

5o 

10 

463726 

470904 

477966 

4849i5 

491754 

498488 

49 

689.4 

ii 

5o5n8 

5n649 

5i8o83 

524423 

530672 

536832 

48 

629.4 

12 

542906 

548897 

5548o6 

56o635 

566387 

572065 

47 

579.  i 

i3 

577668 

583201 

588664 

594059 

599388 

6o4652 

46 

536.2 

i4 

6o9853 

614993 

620072 

625093 

63oo56 

634964 

45 

499.2 

i5 

6398i6 

6446  i  5 

649361 

654o56 

658701 

663297 

44 

467.0 

16 

667845 

672345 

676799 

681208 

685573 

689895 

43 

438.7 

J7 

694173 

698410 

702606 

706762 

710879 

714957 

te 

4i3.6 

18 

718997 

722999 

726965 

730896 

734791 

73865i 

4i 

391.3 

J9 

742478 

746270 

75oo3i 

753758 

757455 

761119 

4o 

371.2 

20 

764754 

768358 

771932 

775477 

778994 

782482 

39 

353.1 

21 

785943 

789376 

792782 

796162 

7995i5 

802843 

38 

336.7 

22 

806146 

809423 

812677 

815906 

819111 

822292 

37 

321.7 

23 

82545i 

828586 

831700 

834791 

83786o 

840907 

36 

3o8.o 

24 

843934 

846939 

849924 

852889 

855833 

858757 

35 

295.4 

25 

861662 

864548 

8674i5 

870262 

873092 

875902 

34 

283.8 

26 

878695 

881470 

884228 

886968 

889690 

892396 

33 

273.1 

27 

895085 

897758 

900414 

9o3o54 

905678 

908287 

32 

263.2 

28 

910879 

9i3457 

916019 

9i8566 

921098 

923616 

3i 

254.0 

29 

926119 

928608 

931082 

933543 

935989 

938422 

3o 

245.4 

3o 

940842 

943248 

94564i 

948020 

950387 

952741 

29 

237.3 

3i 

955082 

957411 

959727 

962031 

964322 

966602 

28 

229.8 

32 

968870 

971126 

97337o 

9756o3 

977824 

980034 

27 

222.7 

33 

982233 

984421 

986598 

988764  1   990919 

993064 

26 

2:6.1 

34 

995198 

997322 

999435 

8.ooi538  3.oo363i 

8.005714 

25 

209.8 

35 

8.007787 

8.009850 

8.011903 

013947   015981 

oi8oo5 

24 

203.9 

36 

O20O2I 

032027 

024023 

026011    027989 

029959 

23 

198.3 

37 

03I9I9 

o3387i 

o358i4 

037749   039675 

041592 

22 

193.0 

38 

o435oi 

o454oi 

047294 

049178   o5io54 

052922 

21 

188.0 

39 

054781 

o56633 

o58477 

o6o3i4 

062142 

o63963 

20 

183.2 

4o 

065776 

067582 

069380 

071171 

072955 

074731 

'9 

178.7 

4i 

076500 

078261 

080016 

081764   o835o4 

o85238 

id 

174.4 

42 

086965 

088684 

090398 

092104   093804 

095497 

J7 

170.3 

43 

097183 

o98863 

ioo537 

102204    io3864 

io55i9 

16 

166.4 

44 

107167 

108809 

no444 

112074    113697 

n53i5 

i5 

162.6 

45 

116926 

ii8532 

I2Ol3l 

121725    I233i3 

124895 

i4 

iSg.  i 

46 

126471 

128042 

129607 

i3n66    132720 

134268 

i3 

155.6 

47 

i358io 

i37348 

138879 

i4o4o6  ]   141927 

143443 

12 

i52.4 

48 

144953 

146458 

147959 

149453 

i  50943 

152428 

II 

149.2 

49 

153907 

155382 

156852 

~  i  583x6 

159776 

i6i23i 

IO 

i46.a 

5o 

162681 

164126 

165566 

167002 

168433 

169859 

9 

i43.3 

5i 

171280 

172697 

174109 

175517 

176920 

178319 

8 

i4o.5 

52 

179713 

i8uo3 

182488 

183869 

185245 

186617 

7 

i37.9 

53 

187985 

189348 

190707 

192062 

I934i3 

194760 

6 

i35.3 

54 

196102 

I9744o 

198774 

200104 

2oi43o 

202752 

5 

i32.8 

55 

204070 

205384 

206694 

2O8OOO 

209302 

210601 

4 

i3o.4 

56 

211895 

2i3i85 

214472 

2l5755 

217034 

218309 

3 

128.1 

57 

219581 

220849 

2221  l3 

223374 

22463i 

225884 

2 

125.  9 

58 

227134 

228380 

229622 

23o86i 

232096 

233328 

I 

123.7 

59 

234557 

235782 

237003 

238221 

239436 

240647 

O 

121.  6 

OOP 

50" 

40" 

30"        20" 

10" 

1 

Co-sine  of  S9  Degrees. 

Min. 

LOGARITHMIC    TANGENTS. 


Min. 

Tangent  of  0  Degree. 

P.  Part 

0" 

10" 

20" 

30"        40"    |    50" 

to  1  •. 

0 

Inf.  Neg. 

5.685575 

5.9866o5 

6.  162696 

6.287635 

6.384545 

59 

I 

6.463726 

6.53o673 

6.588665 

639817 

685575 

•726968 

58 

2 

764756 

7995i8 

83i7o3 

861666 

889695 

916024 

57 

3 

94o847 

964329 

9866o5 

7.007794 

7  O27998 

7.o473o3 

56 

4 

7.o65786 

7.o835i5 

7.ioo548 

116939 

i32733 

147973 

55 

5 

162696 

I76937 

I9O725 

204089 

2i7o54 

229643 

54 

6 

24i878 

253777 

265359 

276640 

287635 

298359 

53 

7 

3o8825 

319044 

329028 

338788 

348333 

357673 

52 

8 

366817 

375772 

384546 

393146 

4oi579 

409852 

5i 

9 

4i797o 

425939 

433764 

44i45i 

449004 

456428 

5o 

10 

463727 

4-70906 

477968 

484917 

49i756 

498490 

49 

689.4 

ii 

5o5i2o 

5n65i 

5i8o85 

524426 

53o675 

536835 

48 

620..  4 

12 

5429o9 

548900 

5548o8 

56o638 

56639o 

5-72068 

47 

579.i 

i3 

577672 

583204 

588667 

5g4o62 

699391 

6o4655 

46 

536.2 

i4 

609857 

614996 

620076 

625097 

63oo6o 

634968 

45 

499.2 

i5 

639820 

644619 

649366 

654o6i    658706 

663302 

44 

467.o 

16 

667849 

67235o 

676804 

681213   685578 

689900 

43 

438.7 

1-7 

6941-79 

698416 

702612 

7o6768   7io885 

•714963 

42 

4i3.6 

18 

•719003 

723oo5 

726972 

•730902   734797 

738658 

4i 

39i.3 

*9 

•742484 

746277 

750037 

753765 

757462 

•76112-7 

4o 

371.3 

20 

76476i 

768365 

771940 

775485 

•7-79002 

•782490 

39 

353.1 

21 

78595i 

789384 

792790 

796i7o 

•799524 

802852 

38 

336.7 

22 

8o6i55 

809433 

812686 

8i59i5 

819120 

822302 

37 

321.7 

23 

825460 

828596 

831710 

8348oi 

83787o 

840918 

36 

3o8.o 

24 

843944 

846950 

849935 

852900 

855844 

858769 

35 

295.4 

25 

861674 

86456o 

867426 

87O274 

873io4 

8759i5 

34 

283.9 

26 

8-78708 

88i483 

884240 

886981 

889-704 

892410 

33 

273.2 

27 

895099 

897772 

900428 

9o3o68 

905692 

9o83oi 

32 

263.2 

28 

910894 

913471 

9i6o34 

9i858i 

921113 

92363i 

3! 

254.0 

29 

926134 

928623 

931098 

933559 

986006 

938439 

3o 

245.4 

3o 

94o858 

943265 

945658 

948o37 

95o4o4 

952758 

29 

237.3 

3i 

gSSioo 

957428 

959745 

962049 

964341 

966621 

28 

229.8 

32 

968889 

97ii45 

973389 

975622 

977844 

980054 

27 

222.7 

33 

982253 

984441 

986618 

988-785 

990940 

993o85 

26 

216.2 

34 

995219 

997343 

999457 

8.ooi56o 

8.oo3653 

3.oo5736 

25 

209.8 

35 

8.007809 

8.009872 

8.011926 

0139-70 

016004 

oi8o29 

24 

2o3.9 

36 

O20044 

O22o5l 

024048 

026o35 

028014 

029984 

23 

i98.3 

37 

031945 

o33897 

o3584o 

o37775 

039-701 

041618 

22 

i93.o 

38 

043527 

045428 

047321 

049205 

o5io8i 

052949 

21 

188.0 

39 

054809 

o56662 

o585o6 

o6o342 

0621-71 

063992 

2O 

i83.3 

4o 

o658o6 

067612 

069410 

O7I2OI 

0-72985 

o7476i 

I9 

178.7 

4i 

076531 

078293 

080047 

O8l795 

o83536 

o8527o 

18 

i74.4 

42 

086997 

088717 

090431 

092l37 

o93837 

095530 

i7 

170.3 

43 

097217 

098897 

100571 

IO2239 

108900 

io5554 

16 

166.4 

44 

107203 

io8845 

no48i 

II2IIO 

n3734 

n5352 

15 

162.7 

45 

116963 

n8569 

120169 

I2i763 

i2335i 

124933 

i4 

i59.i 

46 

i265io 

128081 

129646 

i3i2o6 

i3276o 

i343o8 

i3 

i55.7 

47 

i3585i 

i37389 

138921 

i4o447 

'  141969 

143485 

12 

i52.4 

48 

144996 

i465oi 

i48ooi 

i49497 

15098-7 

l52472 

II 

i49.3 

49 

153952 

i55426 

156896 

i5836i 

159821 

i6i276 

IO 

146.2 

5o 

162727 

164172 

i656i3 

16-7049 

168480 

i699o6 

9 

i43.4 

5i 

171328 

172745 

I74i58 

I75566 

1-76969 

i78368 

8 

i4o.6 

52 

I79763 

i8n53 

182538 

183919 

185296 

186668 

7 

137.9 

53 

i88o36    189400 

190760 

192115 

193466 

I948i3 

6 

135.3 

54 

196156    197494 

198829 

200159 

2oi485 

202808 

5 

i32.8 

55 

204126   ao544o 

206750 

2o8o57 

209359 

2io658 

4 

i3o.4 

56 

211953'    213243 

2i453o 

2i58i4 

21-7093 

2i8369 

3 

128.1 

57 

219641   220909 

222174 

223434 

224692 

225945 

2 

I25.9 

58 

227195   228442 

229685 

230924 

232160 

233392 

I 

123.8 

59 

234621    235846 

237068 

238286 

339502 

24o7i3 

o 

121  .7 

60"        50"    i    40" 

30" 

20" 

10" 

Co-tangent  of  89  Degrees. 

Min. 

LOGARITHMIC    SINES. 


Mia. 

Sine  of  1  Degree. 

P.  Part 

0" 

10" 

20" 

30" 

40"         50" 

to  1". 

O 

8.24i855 

8.  243o6o 

8.244261 

8.245459 

8.246654  8.247845 

59 

119.6 

I 

249033 

250218 

25i4oo 

252578 

253753   254925 

58 

117  7 

2 

256094 

257260 

258423 

259582 

26o739   261892 

5? 

iiS.S 

3 

263042 

264190 

265334 

266475 

267613 

268749 

56 

114.0 

4 

269881 

271010 

272137 

273260 

27438i 

275499 

55 

112.  2 

5 

276614 

277726 

278835 

27994i 

28io45 

282145 

54 

1*0.5 

6 

283243 

284339 

28543i 

286521 

2876o8 

288692 

53 

IOS.8 

7 

289773 

290852 

291928 

298002 

294073  j   295141 

52 

IO7.2 

8 

296207 

297270 

298330 

299388 

3oo443  |   301496 

5i 

105.7 

9 

3o2546 

3o3594 

3o4639 

3o568i 

3o672i    307759 

5o 

104.1 

10 

8.308794 

8.309827 

8.3io857 

8.3n885 

8.312910  8.3i3933 

49 

IO2.6 

ii 

3i4954 

315972 

316987 

3i8ooi 

319012 

320021 

48 

IOI  .2 

12 

321027 

322031 

323o33 

324o32 

325029 

326024 

47 

99.8 

i3 

327016 

328007 

328995 

329980 

330964 

33i945 

46 

98.5 

i4 

332924 

3339oi 

334876 

335848 

3368i9 

337787 

45 

97.1 

i5 

338753 

339717 

340679 

34i638 

342596 

34355i 

44 

95.8 

16 

3445o4 

345456 

3464o5 

34735£ 

348297 

349240  43 

94.6 

17 

35oi8i 

351119 

352056 

352991 

353924 

354855 

42 

93.4 

18 

355783 

3567io 

357635 

358558 

359479 

36o398 

4i 

92.2 

X9 

36i3i5 

36223o 

363i43 

364o55 

364964 

36587i 

4o 

91.0 

20 

8.366777 

8.36768i 

8.368582 

8.369482 

8.370380 

8.  37i277 

39 

89.9 

21 

372171 

373o63 

373954 

374843 

37573o 

3766i5 

38 

88.8 

22 

377499 

37838o 

379260 

38oi38 

38ioi5 

381889 

3? 

87.7 

23 

382762 

383633 

384502 

38537o 

386236 

387100 

36 

86.7 

24 

387962 

388823 

389682 

3oo539 

SgiSgS 

392249 

35 

85.6 

25 

393ioi 

393951 

394800 

395647 

396493 

397337 

34 

84.6 

26 

398I79 

399020 

399859 

4oo696 

4oi532 

402366 

33 

83.7 

27 

403199 

4o4o3o 

4o4859 

4o5687 

4o65i4 

4o7338 

32 

82.7 

28 

408161 

408983 

409803 

410621 

4n438 

412254 

3i 

81.8 

29 

4i3o68 

4i388o 

414691 

4i55oo 

4i63o8 

417114 

3o 

80.8 

3o 

8.417919 

8.418722 

8.419524 

8.42o325 

8.42II23 

8.421921 

29 

80.0 

3i 

422717 

4235ii 

4243o4 

425o96 

425886 

426675 

28 

79..! 

32 

427462 

428248 

429032 

429815 

43o597 

43i377 

27 

78.2 

33 

432i56 

432934 

4337io 

434484 

435257   436029 

26 

77-4 

34 

4368oo 

437569 

438337 

439103 

439868 

44o632 

25 

76.6 

35 

44i394 

442i56 

442915 

443674 

44443i 

445i86 

24 

75.8 

36 

44594i   446694 

447446 

448196 

448946 

449694 

23 

75.o 

3? 

45o44o   45u86 

451930 

452673 

4534i4 

454i54 

22 

74.2 

38 

454893   45563i 

456368 

457io3 

457837 

458570 

21 

73.5 

39 

4593oi   46oo32 

46o76i 

461489 

462215 

462941 

2O 

72-7 

4o 

8.463665  8.464388 

8.465no 

8.46583o 

8.46655o 

8.467268 

J9 

72.O 

4i 

467985   468701 

469416 

47oi29 

470841 

47i553 

18 

71.3 

42 

472263   472971 

473679 

474386 

475091 

475795 

*7 

70.6 

43 

476498   477200 

4779oi 

478601 

479299 

479997 

16 

69.9 

44 

48o693  !   48  i  388 

482083 

482776 

483467 

484i58 

i5 

69.2 

45 

484848   485536 

486224 

486910 

487596 

488280 

i4 

68.6 

46 

488963   489645 

490326 

491006 

49i685 

492363 

i3 

67.9 

4? 

498040   493715 

494390 

495o64 

495736 

496408 

12 

67.3 

48 

497078   497748 

498416 

499084 

49975o 

5oo4i6 

II 

66.7 

49 

5oio8o 

501743 

5o24o5 

5o3o67 

5o3727 

5o4386 

IO 

66.1 

5o 

8.5o5o45 

8.5o57O2 

8.5o6358 

8.  507014 

8.5o7668 

8.5o832i 

9 

65.5 

5i 

508974 

509625 

5io275 

510925 

5ii573 

5l222I 

8 

64.  9 

52 

512867 

5i35i3 

5i4i57 

5i48oi 

5  i5444 

5i6o86 

7 

64.3 

53 

516726 

5i7366 

5i8oo5 

5i8643 

519280 

519916 

6 

63.7 

54 

52o55i 

521186 

521819 

52245i 

523o83 

5237i3 

5 

63.2 

55 

524343 

524972 

525599 

526226 

526852 

527477 

4 

62.6 

56 

528102 

528725 

529347 

529969  j 

53o59o 

531209 

3 

62.1 

5? 

531828 

532446 

533o63 

533679 

534295 

534909 

2 

61.6 

58 

535523 

536i36 

536747 

537358 

537969 

538578 

I 

61.1 

59 

539186  :   539794 

54o4oi 

54ioo7 

54i6i2 

542216 

O 

6o.5 

60"       50" 

40" 

30" 

20" 

10" 

Co-sine  of  88  Degrees. 

Min. 

LOGARITHMIC    TANGENTS. 


Min. 

Tangent  of  1  Degree. 

P.  Part 

0" 

10" 

20" 

30" 

40" 

50" 

to  1". 

0 

8.241921 

8.243126 

8.244328 

8.245526 

8.246721 

8.247913 

59 

II9-7 

I 

249102 

250287 

251469 

252648 

253823 

254996 

58 

117.7 

2 

256i65 

25733i 

258494 

259654 

260811 

261965 

57 

n5,8 

3 

263n5 

264263 

2654o8 

266549 

267688 

268824 

56 

n4.o 

4 

269956 

271086 

272213 

273337 

274458 

275576 

55 

112.  2 

5 

276691 

277804 

278913 

280020 

281124 

282225 

54 

no.  5 

6 

283323 

284419 

2855i2 

286602 

287689 

288774 

53 

io8.9 

7 

289856 

290935 

292012 

293086 

294157 

295226 

52 

107.2 

8 

296292 

297355 

298416 

299474 

3oo53o 

3oi583 

5i 

105.7 

9 

3o2634 

3o3682 

304727 

305770 

3o68u 

307849 

5o 

104.2 

10 

8.3o8884 

8.309917 

8.310948 

8.311976  8.3i3oo2 

8.3i4o25 

49 

102.7 

ii 

3i5o46 

3i6o65 

317081 

3i8o95 

319106 

32on5 

48 

loi.S 

12 

32II22 

322127 

323129 

324l29 

325i26 

326121 

47 

99-8 

i3 

327II4 

328io5 

329093 

33oo8o  |   33io64 

332045 

46 

98>5 

U 

333025 

334oo2 

334977 

33595o  !   336921 

337890 

45 

97-2 

i5 

338856 

339821 

340783 

34i743 

342701 

343657 

44 

95.9 

16 

3446io 

345562 

3465i2 

347459 

3484o5 

349348 

43 

94.6 

J7 

350289 

351229 

352i66 

353ioi 

354o35 

354966 

42 

93.4 

18 

355895 

356823 

357748 

35867i 

SSgSgS 

36o5i2 

4i 

92.2 

*9 

36i43o 

362345 

363259 

364171 

365o8i 

365988 

4o 

9I.I 

20 

8.866895 

8.367799 

8.368701 

8.369601 

8.37o5oo 

8.371397 

39 

89.9  ^ 

21 

372292 

373i85 

374076 

374965 

375853 

376738 

38 

88.8 

22 

377622 

3785o4 

379385 

380263 

38n4o 

382oi5 

37 

87.8 

•23 

382889 

383760 

38463o 

385498 

386364 

387229 

36 

86.7 

24 

388092 

388953 

389813 

390670 

391526 

392381 

35 

85.7 

25 

393234 

394o85 

394934 

395782 

396628 

397472 

34 

84.7 

26 

3983i5 

399156 

399996 

4oo834 

401670 

4o25o5 

33 

83.7 

27 

4o3338 

404.170 

4o5ooo 

4o5828 

4o6655 

407480 

32 

82.8 

28 

4o83o4 

409126 

409946 

410765 

4n583 

412399 

3i 

81.8 

29 

4i32i3 

414026 

4i4837 

4i5647 

4i6456 

417263 

3o 

80.  9 

3o 

8.4i8o68 

8.418872 

8.419674 

8.420475 

8.421274 

8.422072 

29 

80.0 

3i 

422869 

423664 

424458 

42525o 

426041 

42683o 

28 

79.i 

32 

427618 

428404 

4a9i89 

429973 

43o755 

43i536 

27 

78.3 

33 

4323i5 

433093 

433870 

434645 

4354i9 

436191 

26 

77.5 

34 

436962 

437732 

4385oo 

439267 

44oo33 

440797 

25 

76.6 

?5 

44i56o 

442322 

443082 

44384i 

444599 

445355 

24 

75.8 

36 

446no 

446864 

447616 

448368 

449117 

449866 

23 

75.o 

37 

45o6i3 

45i359 

452io4 

452847 

453589 

45433o 

22 

74,3 

38 

455070 

4558o8 

456545 

457281 

458oi6 

458749 

21 

73.5 

39 

459481 

460212 

46o942 

461670 

462398 

463i24 

2O 

72.8 

4o 

8.463849 

8.464572 

8.465295 

8.  466016 

8.466736 

8.  467455 

*9 

72.1 

4i 

468172 

468889 

4696o4 

47o3i8 

47io3i 

471743 

18 

7i.3 

42 

472454 

473i63 

473872 

474579 

475285 

475990 

J7 

70.7 

43 

476693 

477396 

478o97 

478798 

479497 

480195 

16 

70.0 

44 

480892 

48  i  588 

482283 

482976 

483669 

48436o 

i5 

69.3 

45 

485o5o 

48574o 

486428 

487115 

487801 

488486 

i4 

68.6 

46 

489170 

489852 

49o534 

491215 

491894 

492573 

i3 

68.0 

4? 

49325o 

493927 

4946o2 

495276 

495949 

496622 

12 

67.4 

48 

497293 

497963 

498632 

499300 

499967 

5oo633 

II 

66.8 

49 

501298 

501962 

5o2625 

503287 

5o3948 

5o46o8 

IO 

66.1 

5o 

8.  505267 

8.5o5925 

8.5o6582 

8.  507238 

8.507893 

8.5o8547 

9 

65.5 

5i 

509200 

509852 

5io5o3 

5m53 

5n8o2 

5i245i 

8 

65.o 

62 

5  i  3098 

5i3744 

5i4389 

5i5o34 

5i5677 

5i632o 

7 

64.4 

53 

516961 

517602 

518241 

5i888o 

5i95i8 

52oi54 

6 

63.8 

54 

520790 

52i425 

522O59 

522692 

523324 

523956 

5 

63.3 

55 

5a4586 

5252i5 

525844 

526472 

527098 

527724 

4 

62.7 

56 

528349 

528973 

529596 

53o2i8 

53o84o 

53i46o 

3 

62.2 

57 

532o8o 

532698 

5333i6 

533933 

534549 

535i64 

2 

61.6 

58 

535779 

536392 

537oo5 

5376i7 

538227 

538837 

I 

61.1 

59 

539447 

54oo55 

540662 

541269 

54i875 

54248o 

O 

60.6 

fiO»        50"    |    40" 

30" 

20" 

10" 

Co-tangent  of  88  Degrees. 

Min. 

•26 


LOGARITHM    c    SINES. 


i 

Sine  of  2  Degrees. 

d 

Sine  of  3  Degrees. 

8 

0" 

10" 

20" 

30' 

40" 

50" 

9 

0" 

10" 

20" 

30" 

40" 

50" 

0 

8.542819 

3422 

4023 

4624 

5224 

5823 

59 

o 

8.7i88oo 

92O2 

96o3 

...4 

•  4o4 

.8o4 

59 

1 

6422 

7oi9 

7616 

8212 

8807 

94oi 

58 

I 

8.  72I204 

i6o3 

20O2 

2401 

2799 

3i97 

58 

2 

9995 

.587 

1179 

I770 

236! 

295o 

57 

2 

3595 

3992 

4389 

4785 

5i8i 

5577 

57 

3 

8  553539 

4126 

4?i3 

53oo 

5885 

647o 

56 

3 

5972 

6367 

6762 

7i56 

755o 

7943 

56 

4 

7054 

7637 

8219 

8801 

938i 

996i 

55 

4 

8337 

8729 

9I22 

95i4 

9906 

•297 

55 

5 

8.56o54o 

1119 

1696 

2273 

2849 

3425 

54 

5 

8.73o688 

io79 

i469 

i859 

2249 

2638 

54 

6 

3999 

4573 

5i46 

5719 

629o 

6861 

53 

6 

3027 

34i6 

38o4 

4l92 

4579 

4967 

53 

7 

743  1 

8000 

8569 

9i37 

97o4 

.27O 

52 

7 

5354 

574o 

6126 

65i2 

6898 

7283 

52 

8 

8.570836 

i4oi 

1965 

2528 

3o9i 

3653 

5i 

8 

7667 

8o52 

8436 

8820 

92o3 

9586 

5i 

9 

4214 

4774 

5334 

5893 

645  1 

7oo9 

5o 

9 

9969 

.352 

•  734 

in5 

i497 

i878 

5o 

10 

7566 

8122 

8678 

9232 

9786 

.34o 

49 

10 

8.742259 

2639 

3oi9 

3399 

3778 

4i57 

49 

ii 

8.  58o892 

1  444 

i995 

2546 

3o96 

3645 

48 

ii 

4536 

49i4 

5293 

5670 

6o48 

6425 

48 

12 

4i93 

474i 

5288 

5834 

638o 

6925 

47 

12 

6802 

7178 

7554 

793o 

83o5 

8680 

47 

i3 

7469 

8oi3 

8556  9098 

964o 

.181 

46 

i3 

9o55 

943o 

98o4 

.178 

.55i 

.924 

46 

i4 

8.590721 

1260 

1799  2338 

2875 

34i2 

45 

i4 

8.751297 

i67o 

2042 

24i4 

2786 

3i57 

45 

i5 

3948 

4484 

5oi9!5553 

6087 

66i9 

44 

i5 

3528 

3898 

4269 

4639 

5oo8 

5378 

44 

16 

7152 

7683 

8214 

8745 

9274 

98o3 

43 

16 

5747 

6116 

6484 

6852 

7220 

7587 

43 

J7 

8.6oo332 

0859 

i387 

I9i3 

2439  2964 

42 

ll 

7955 

832i 

8688 

9o54 

942O 

9786 

42 

18 

3489 

4012 

4536  5o58 

558o6io2 

4i 

18 

8.760151 

o5i6 

0881 

1245 

1609 

i973 

4i 

X9 

6623 

7143 

76628181 

8699 

92I7 

4o 

J9 

2337 

27OO 

3o63 

3425 

3787 

4i49 

4o 

20 

9734 

.25i 

.766  1282 

i796 

23lO 

39 

20 

45ii 

4872 

5234 

5594 

5955 

63i5 

39 

21 

8.612823 

3336 

3848  436o 

487i 

538i 

38 

21 

6675 

7o34 

7394 

7752 

8111 

8469 

38 

22 

5891 

64oo 

69097417 

7924 

843  1 

37 

22 

8828 

9i85 

9543 

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23 

8937 

9442 

9947  .452 

.956 

i459 

36 

23 

8.77o97o 

i326 

1681 

2o37 

2392 

2747 

36 

24 

8.621962 

2464 

2965  3466 

3966 

4466 

35 

24 

3ioi 

3456 

38io 

4i63 

45i7 

487o 

35 

25 

4965 

5464 

5962  6459 

6956 

7453 

34 

25 

5223 

5575 

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6279 

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6982 

34 

26 

7948 

8444 

8938^432 

9926 

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33 

26 

7333 

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33 

27 

8.630911 

i4o3 

i8942385 

2875 

3365 

32 

27 

9434 

9783 

.132 

.48o 

.829 

"77 

32 

28 

3854 

4342 

483o53i7 

58o4 

6291 

3i 

28 

8.78i524 

1872 

22I9 

2566 

2912 

3259 

3i 

29 

6776 

7262 

77468230 

8714 

9i97 

3o 

29 

36o5 

395i 

4296 

464i 

4986 

533i 

3o 

3o 

9680 

.162 

.643  1124 

i6o4 

2084 

29 

3o 

5675 

6oi9 

6363 

67°7 

7o5o 

7393 

29 

3i 

8.642563 

3o42 

3520  3998 

4475 

4952 

28 

3i 

7736 

8078 

8421 

8762 

9104 

9446 

28 

32 

5428 

59o4 

63796854 

7328 

7801 

27 

32 

9787 

.128 

.468 

.808 

1149 

i486 

27 

33    8274 

8747 

9219  9690 

.161 

.632 

26 

33 

8.79i828 

2167 

25o6 

2845 

3i83 

352i 

26 

34|8.65iio2 

i57i 

2040  25o8 

2976 

3444 

25 

34 

3859 

4i97 

4534 

4872 

52o8 

5545 

25 

351    39n 

4377 

484353o8 

5773 

6238 

24 

35 

588i 

6218 

6553 

6889 

7224 

7559 

24 

36    6702 

7i65 

7628  8090 

8552 

9014 

23 

36 

7894 

8229 

8563 

8897 

9231 

9564 

23 

3?|    94?5 

9935 

.395  .855 

:3i4 

1772 

22 

37 

9897 

.230 

.563 

.896 

1228 

i56o 

22 

38J8.662230 

2688 

3i4536o2 

4o58 

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21 

38 

8.801892 

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39 

4968 

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5877633i 

6784 

7237 

2O 

39 

3876 

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4536 

4866 

5i95 

5524 

20 

4o 

7689 

8i4i 

8592  9«43 

9494 

9944 

19 

4o 

5852 

6181 

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7i65 

7492 

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4i 

8.670393 

0842 

1291  1739 

2187 

2634 

18 

4i 

7819 

8i46 

8473 

8799 

9126 

945i 

18 

42 

3o8o 

3527 

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4863 

53o7 

17 

42 

9777 

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.428 

.753 

1078 

1402 

17 

43 

575i 

6i94 

6638  7o8o 

7522 

7964 

16 

43 

8.811726 

2o5o 

2374 

2698 

3021 

3344 

16 

44 

84o5 

8846 

9286!9726 

.166 

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i5 

44 

3667 

3989 

43i2 

4634 

4956 

5277  i5 

45 

8.  68io43 

i48i 

19192356 

2793 

323o 

i4 

45 

5599 

5920 

6241 

656i 

6882 

7202'  i4 

46 

3665 

4ioi 

45364971 

54o5 

5838 

i3 

46 

7522 

7841 

8161 

848o 

8799 

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4? 

6272 

67o5 

71377569 

8001 

8432 

12 

47 

9436 

9755 

..73 

.390 

.7o8 

I025|I2 

48 

8863 

9a93 

9723 

.152 

.58i 

1010 

II 

48 

8.821343 

i659 

i976 

2292 

2609 

2925 

II 

49 

8.691438 

1866 

2293 

2720 

3i46 

3572 

IO 

49 

324o 

3556 

387i 

4i86 

45oi 

48i6 

IO 

5o 

3998 

4423 

4848 

5272 

5696 

6120 

9 

5o 

5i3o 

5444 

5758 

6072 

6385 

6698 

9 

Si 

6543 

6966 

7388 

7810 

8232 

8653 

8 

5i 

7011 

7324 

7637 

7949 

8261 

8573 

8 

52 

9°73 

9494 

99i3 

.333 

.752 

1171 

7 

52 

8884 

9i96 

95°7 

9818 

.  129 

.439 

7 

53 

8.7oi589 

2OO7 

2424 

2841 

3258 

3674 

6 

53 

8.83o749 

1060 

i369 

1679 

1988 

2298 

6 

54 

4o9o 

45o5 

4920 

5335 

5749 

6i63 

5 

54 

2607 

29i5 

3224 

3532 

384o 

4i48 

5 

55 

6577 

6990 

7402 

78i5 

8226 

8638 

4 

55 

4456 

4763 

5070 

5377 

5684 

599i 

4 

56 

9o49 

9460 

9870 

.280 

.69o 

1099 

3 

56 

6297 

66o3 

69o9 

72l5 

7520 

7825 

3 

5? 

8.711507 

1916 

2324 

273l 

3i39 

3546 

2 

57 

8i3o 

8435 

874o 

9044  9348 

9652 

2 

58 

3952 

4358 

4764 

5i69 

5574 

5979 

I 

58 

9956 

.260 

.563 

.866  1169 

1472 

I 

59 

6383 

6787 

7I90 

7593 

7996 

8398 

O 

59 

8.841774 

2O76 

2378 

2680J2982 

3283 

O 

60" 

50" 

40" 

30" 

20" 

10" 

a 

60" 

50"   40" 

30"  |  20" 

10" 

g 

Co-sine  of  87  Degrees. 

s 

Co-sine  of  86  Degrees. 

S 

.<  1"  2''  3"  4"  5"  6"  7"  8"  9" 

(  I"  2"  3"  4"  5"  6"  7"  8"  9" 

irt}  48  96  145  192  241  289  33$  386  434 

Lrt}  34  69  103  138  172  207  241  275  310 

LOGARITHMIC    TANGENTS. 


27 


B 

Tangent  of  2  Degrees.  - 

a 

Tangent  of  3  Degrees. 

9 

0" 

10" 

20" 

30"  |  40 

50" 

& 

0" 

10" 

20" 

30" 

40"   50" 

o 

8.543o84 

3687 

4289 

4891 

5492 

6o92 

59 

o 

8.719396 

9798 

.2OI 

.6o3 

ioo4 

i4o5 

59 

I 

6691 

7289 

7887 

8483 

9079 

9674 

58 

I 

8.721806 

2207 

2607 

3oo7 

34o6 

38o5 

58 

2 

8.  55o268 

0862 

i454 

2046 

2637 

3227 

57 

2 

4204 

i6o2 

5ooo 

5397 

5-794 

6191 

57 

3 

3817 

44o5 

4993 

558o 

6166 

6752 

56 

3 

6588 

6984 

7380 

7775 

8i7o 

8565 

56 

4 

7336 

7920 

85o3 

9o85 

9667 

248 

55 

4 

8959 

9353 

9746 

533 

925 

55 

5 

8.56o828 

i4o7 

i985 

2563 

3i4o 

(716 

54 

5 

8.73i3i7 

7°9 

2IOI 

2492 

2883 

3273 

54 

6 

4291 

4866 

544o 

6oi3 

6585 

7i57 

53 

6 

3663 

4o53 

4442 

483i 

5220 

56o8 

53 

7 

7727 

8298 

8867 

9435 

...3 

57o 

52 

7 

5996 

6384 

6771 

7i58 

7545 

793i 

52 

8 

8.57n37 

1702 

2267 

2832 

3395 

3958 

5i 

8 

83i7 

87o3 

9088 

9473 

9858 

242 

5i 

9 

452O 

5o8i 

5642 

6201 

6760 

7319 

5o 

9 

8.740626 

1009 

i393 

1776 

2i58 

254o 

5o 

10 

7877 

8434 

8990 

9545 

.  IOO 

.654 

J9 

10 

2922 

33o4 

3685 

4o66 

4447 

4827 

49 

ii 

8.58i2o8 

1760 

2312 

2864 

34i4 

3964 

ii 

5207 

5586 

5g66 

6344 

6723 

7101 

48 

-12 

45i4 

5o62 

56io 

6i57 

67o4 

7249 

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12 

7479 

7857 

8234 

8611 

8988 

9364 

47 

i3 

7795 

8339 

8883 

9426 

9968 

.5io 

46 

i3 

9740 

.116 

.491 

.866 

1241 

i6i5 

46 

i4 

i59x 

2l3l 

26-70 

3208 

3746 

45 

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8.751989 

2363 

2736 

3109 

3482 

3855 

45 

i5 

4283 

4820 

5355 

589o 

6425 

6959 

44 

i5 

4227 

4599 

4970 

534i 

5712 

6o83 

44 

16 

7492 

8024 

8556 

9o87 

9618 

.147 

43 

16 

6453 

6823 

7i93 

7562 

7931 

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ll 

8.600677 

1205 

i733 

2260 

2787 

33i3 

42 

ll 

8668 

9036 

9404 

9771 

.i39 

.5o5 

42 

18 

3839 

4363 

4887 

54n 

5934 

6456 

4i 

18 

8.760872 

1238 

1604 

1970 

2335 

2700 

4i 

19 

6978 

7499 

8019 

8539 

9o58 

9576 

4o 

19 

3o65 

3429 

3793 

4i57 

452O 

4884 

4o 

20 

8.610094 

0612 

1128 

1  644 

2160 

2675 

39 

20 

5246 

56og 

597i 

6333 

6695 

7o56 

39 

21 

3i89 

3702 

42  1  5 

4728 

524o 

575i 

38 

21 

7417 

7778 

8i39 

8499 

8859 

9218 

38 

22 

6262 

6772 

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8298 

8806 

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22 

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1370 

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23 

93i3 

9819 

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i335 

1839 

36 

23 

8.77i727 

2o85 

2442 

2798 

3i55 

35n 

36 

24 

8.622343 

2846 

3348 

385o 

435i 

4852 

35 

24 

3866 

4222 

4577 

4932 

5287 

564i 

35 

25 

5352 

585i 

635o 

6849 

7346 

7844 

34 

25 

5995 

6349 

6702 

7o56 

74o9 

7761 

34 

26 

834o 

8836 

9332 

9827 

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.8x5 

33 

26 

8n4 

8466 

8817 

9169 

9520 

9871 

33 

27 

8.63i3o8 

1801 

2293 

2785 

3276 

3766 

32 

27 

8.780222 

o572 

0922 

1272 

1622 

1971 

32 

28 

4256 

4746 

5235 

5723 

6211 

6698 

3i 

28 

2320 

2669 

3017 

3365 

37i3 

4o6i 

3i 

29 

7i84 

7671 

8i56 

864i 

9I26 

9610 

3o 

29 

44o8 

4755 

5  1  02 

5448 

5794 

6i4o 

3o 

3o 

8.640093 

o576 

io58 

i54o 

2O2I 

25O2 

29 

3o 

6486 

683i 

7177 

752I 

7866 

8210 

29 

3i 

2982 

3462 

394i 

4420 

4898 

5376 

28 

3i 

8554 

8898 

9242 

9585 

9928 

.271 

28 

32 

5853 

6329 

68o5 

728l 

7756 

823o 

27 

32 

8.790613 

o955 

1297 

i639 

1980 

2321 

27 

33 

87o4 

91-78 

965i 

.  123 

.595 

1067 

26 

33 

2662 

3oo3 

3343 

3683 

4023 

4362 

26 

34 

8.65i537 

2008 

24-78 

2947 

34i6 

3884 

25 

34 

47oi 

5o4o 

5379 

57i8 

6o56 

6394 

25 

35 

4352 

4820 

5286 

5753 

62I9 

6684 

24 

35 

673i 

7069 

74o6 

7743 

8o79 

84i6 

24 

36 

7149 

76i3 

8o77 

854i 

9oo4 

9466 

23 

36    8752 

9088 

g423 

9759 

..94 

.429 

23 

3? 

9928 

.389 

.85o 

i3n 

1771 

2230 

22 

37 

8.800763 

1098 

1432 

i765 

2099 

2432 

22 

38 

8.662689 

3i48 

36o6 

4o63 

4520 

4977 

21 

38 

2765 

3o98 

343  1 

3763 

4095 

4427 

21 

39 

5433 

5889 

6344 

6799 

7253 

7707 

2O 

39 

4758 

Sogo 

5421 

575i 

6082 

6412 

20 

4o 

8160 

86i3 

9065 

95i7 

9968 

19 

4o 

6742 

7072 

7/J02 

773i 

8060 

8389 

19 

4i 

8.670870 

1320 

I769 

2218 

2667 

3ii5 

18 

4i 

8717 

9o46 

9374 

97oi 

..29 

.356 

18 

42 

3563 

4oio 

4457 

4903 

5349 

5794 

17 

42 

8.8io683 

IOIO 

i337 

i663 

1989 

23i5 

17 

43 

6239 

6684 

7I28 

7572 

8oi5 

8457 

16 

43 

2641 

2966 

3291 

36i6 

4265 

16 

44 

8900 

9341 

9783 

.222 

.664 

1104 

i5 

44 

4589 

4913 

5237 

556o 

5884 

6207 

i5 

45 

8.68i544 

i983 

2422 

2860 

3298 

3735 

i4 

45 

6529 

6852 

7174 

?423 

78i8 

8i4o 

i4 

46 

4172 

46o8 

5o44 

5480 

5gi5 

635o 

i3 

46 

846i 

8782 

910: 

9744 

..64 

i3 

47 

6784 

-7218 

7652 

8o85 

85i7 

895o 

12 

47 

8.820382 

0703 

102: 

1  342 

1661 

1980 

12 

48 

9381 

98i3 

.244 

.674 

1104 

i534 

II 

48 

229^ 

2617 

2935 

3253 

357o 

3888 

II 

49 

8.691963 

2392 

2820 

3248 

3675 

4io3 

10 

49 

42o5 

4522 

4838 

5i55 

547i 

5787 

10 

5o 

4529 

4956 

538i 

58o7 

6232 

6656 

9 

5o 

6io3 

64i8 

6733 

7049 

7363 

7678 

9 

Si 

7081 

75o2 

7928 

835i 

8773 

9i95 

8 

5i 

7992 

83o7 

8621 

8934 

924^ 

956i 

8 

52 

9617 

..38 

.880 

i3oo 

1720 

7 

52 

9874 

.187 

.5oo 

.812 

1  1  22 

i436 

7 

53 

8.702139 

2558 

29-76 

33g5 

38i2 

4230 

6 

53 

8.83i748 

2059 

237I 

2682 

2992 

33o3 

6 

54 

4646 

5o63 

5479 

5895 

63io 

6725 

5 

54 

36i3 

3924 

4234 

4543 

4853 

5i62 

5 

55 

7i4o 

7554 

7967 

838i 

8794 

9206 

4 

55 

547i 

578o 

6089 

6397 

67o5 

701^ 

4 

56 

9618 

..3o 

.442 

.853 

1263 

1672 

3 

56 

732I 

7629 

7936 

8243 

855o 

8857 

3 

57 

8.7i2o83 

2493 

2902 

33xi 

37i9 

4127 

2 

57 

9i63 

9470 

9776 

..81 

.387 

.692 

2 

58 

4534 

4942 

5348 

5755 

6161 

6567 

I 

58 

8.840998 

i3o3 

160-7 

1912 

2216 

2521 

I 

59 

69-72 

7377 

7781 

8186 

8589 

8993 

O 

59 

2825 

3i28 

3432 

3735 

4o38 

434i 

O 

60" 

50" 

40" 

30" 

20" 

10" 

rt 

60" 

50" 

40" 

30" 

20" 

10" 

d 

Co-tangent  of  87  Degrees. 

1 

Co-tangent  of  86  Degrees. 

9 

,  .5  I"  2"  3"  4"  5"  6"  7"  8"  9" 

C  1"  2"  3"  4"  5"  6"  7"  8"  9" 

lrl}  48  97  145  193  242  290  338  387  435 

drt  {  35  69  104  138  173  207  242  276  311 

LOGARITHMIC    SINES. 


1 

Sine  of  4  Degrees. 

Sine  of  5  Degrees. 

H 

0" 

10" 

20" 

30" 

40" 

50" 

0" 

10"   20" 

30" 

40" 

50" 

o 

8.843585 

3886 

4i86 

4487 

4?«7 

6087 

59 

o 

8.940296 

o537 

0777 

IOI7 

1258 

1498 

59 

i 

5387 

5687 

5987 

6286 

6585 

6884 

58 

I 

173? 

1977 

2217 

2457 

2696 

2935 

58 

2 

7i83 

748  1 

7780 

80-78 

8376 

8673 

57 

2 

8174 

34x3 

3652 

3891 

4129 

4368 

57 

3 

8971 

9268 

9565 

9862 

.i59 

.455 

56 

3 

46o6 

4844 

5o83 

532i 

5558 

5796 

56 

4 

8.85o75i 

io47 

1  343 

i639 

i934 

2229 

55 

4 

6o34 

6271 

65o8 

6745 

6982 

7219 

55 

5 

2525 

2819 

3n4 

34o8 

37o3 

3997 

54 

5 

7456 

7693 

7929 

8166 

8402 

8638 

54 

6 

4291 

4584 

4878 

5i7i 

5464 

5757 

53 

6 

8874 

9110 

9345 

958i 

9817 

..52 

53 

7 

6049 

6342 

6634 

6926 

7218 

52 

7 

8.950287 

O522 

°757 

0992 

1227 

i46i 

5a 

8 

7801 

8092 

8383 

8674 

8965 

9255 

5i 

8 

1696 

1930 

2164 

2398 

2632 

2866 

5i 

9 

9546 

9836 

.126 

.4i5 

.705 

994 

5o 

9 

3ioo 

3333 

3567 

38oo 

4o33 

4266 

5o 

10 

8.861283 

I572 

1861 

2149 

2438 

2726 

49 

10 

4499 

4732 

4965 

5197 

5429 

5662 

49 

ii 

3oi4 

3302 

3589 

3877 

4i64 

445  1 

48 

ii 

5894 

6126 

6358 

65go 

6821 

7o53 

48 

12 

4738 

5o24 

53n 

5597 

5883 

6169 

47 

12 

7284 

75i6 

7747 

7978 

8209 

844o 

47 

i3 

6455 

674o 

7025 

73io 

7595 

7880 

46 

i3 

8670 

8901 

9i3i 

9362 

9592 

9822 

46 

i4 

8i65 

8449 

8733 

901-7 

93oi 

9585 

45 

i4 

8.960052 

0282 

o5n 

0741 

0970 

I2OO 

45 

i5 

9868 

.  i5i 

.434 

•717 

IOOO 

1282 

44 

i5 

1429 

i658 

188-7 

2116 

2344 

2573 

44 

16 

8.87i565 

i847 

2129 

2410 

2692 

2973 

43 

16 

2801 

3o3o 

3258 

3486 

3714 

3942 

43 

17 

3255 

3536 

38i7 

409-7 

4378 

4658 

42 

17 

4170 

4397 

4625 

4852 

5o8o 

53o7 

42 

18 

4938 

52i8 

5498 

5777 

6o57 

6336 

4i 

18 

5534 

576i 

5987 

6214 

644i 

6667 

4i 

19 

66i5 

6894 

7172 

745i 

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6 

54 

1  544 

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54 

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2979 

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55 

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3260 

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4 

55 

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4969 

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56 

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4602 

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5007 

5209 

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3 

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5942 

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6428 

6671 

6914 

7i56 

2 

57 

56i3 

58i5 

6017 

6219 

6421 

6622 

2 

58 

7398 

7641 

7883 

8i25 

8366 

8608 

I 

58 

6824 

7025 

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7428 

7629 

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I 

59 

885o 

9o9i 

9332 

9573 

9814 

..55 

0 

59 

8o3i 

8232 

8433 

8633 

8834 

qoSt 

0 

60" 

50" 

40" 

30" 

20" 

10" 

^ 

60" 

50" 

40" 

30" 

20" 

10" 

d 

Co-sine  of  85  Degrees. 

3 

Co-sine  of  84  Degrees. 

fl 

s, 

/  1  //  nil  o//  411   K.II   ell   fll   oil   nil 
P  PortJ  l<J-*45b789 

ITI\  27  53  80  107  134  160  187  214  241 

p  p.  <  1"  2"  3"  4"  5"  6"  7"  8"  9" 
1  n\  22  44  66  87  109  131  153  175  197 

LOGARITHMIC    TANGENTS. 


1 

Tangent  of  4  Degrees. 

d 

Tangent  of  5  Degrees. 

2 

0" 

10" 

20" 

30" 

40" 

50" 

S 

0" 

10" 

20" 

30"   40"  )  50" 

o 

.844644 

4946 

5248 

555i 

5852 

6i54 

59 

O 

8.94i952 

2I94 

2437 

2679 

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3i63 

59 

I 

6455 

6757 

7o58 

7358 

7659 

7959 

58 

I 

34o4 

3646 

3888 

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4370 

46n 

58 

2 

8260 

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8859 

9l59 

9458 

9758 

57 

2 

4852 

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57 

3 

8.85oo57 

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0952 

1260 

1  548 

56 

3 

6295 

5535 

6775 

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7255 

7494 

56 

4 

1  846 

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2738 

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3332 

55 

4 

7734 

7973 

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8690 

8929 

55 

5 

3628 

3925 

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54 

5 

9168 

9406 

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121 

359 

54 

6 

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6288 

6583 

6877 

53 

6 

8.950597 

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547 

1784 

53 

7 

7171 

7465 

7759 

8o53 

8346 

8639 

52 

7 

2021 

2258 

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2968 

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52 

8 

8932 

9225 

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8 

344i 

3677 

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4385 

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9 

8.860686 

0977 

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1861 

2142 

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9 

4856 

5092 

5327 

5562 

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10 

2433 

2723 

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3883 

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6267 

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7205 

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53 

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53 

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3856 

4062 

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54 

3i34 

338i 

3629 

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5 

54 

4268 

4474 

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4886 

5091 

5297 

5 

55 

46i6 

4862 

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5355 

56oi 

5847 

4 

55 

55o2 

57o7 

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6118 

6323 

6528 

4 

56 

6o93 

6339 

6584 

683o 

7075 

7320 

3 

56 

6732 

6937 

7l42 

7346 

755i 

7755 

3 

57 

7565 

7810 

8o55 

8299 

8544 

8788 

2 

57 

7959 

8i64 

8368 

8572 

8776 

8979 

2 

58 

9o32 

9276 

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9764 

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.251 

I 

58 

9i8c 

9387 

959o 

9794 

9997 

.200 

I 

59 

8.94o494 

0738 

o98i 

I22/i 

1467 

1709 

O 

59 

9.o2o4o3 

0606 

o8o9 

1012 

I2l5 

1418 

O 

60" 

50" 

40" 

30" 

20" 

10" 

£3 

60" 

50" 

40" 

30* 

20" 

10" 

a 

Co-tangent  of  85  Degrees. 

1 

Co-tangent  of  84  Degrees. 

i 

p  p  t<  1"2"  3"  4"  5"  6"  7"  8"  9" 

p  p  ,  (  1"  2"  3"  4"  5"  6"  7"  9"  9" 

irl\  27  54  81  108  135  162  188  215  242 

'  art£22  44  66  88  110  132  154  177  199 

LOGARITHMIC    SINES. 


A 

Sine  of  6  Degrees. 

J 

Sine  of  7  Degrees. 

s 

0" 

10" 

20" 

30" 

40"  |  W 

8 

0" 

10"   20" 

30" 

40" 

50" 

o 

9.019235 

9435 

9635 

983!> 

..35 

.235 

59 

0 

9.086894 

6066 

6237 

6409 

6680 

675i 

59 

I 

9.o2o435 

o635 

o834 

io34 

1233 

i433 

58 

I 

6922 

7°93 

7264 

7435 

7606 

7777 

58 

2 

:632 

i83i 

2o3o 

2229 

2428 

2627 

57 

2 

7947 

8118 

8288 

8459 

8629 

8800 

57 

3 

2826 

3024 

3223 

342i 

36i9 

38i8 

56 

3 

89709140 

93io 

9480 

965i 

9820 

56 

4 

4oi6 

42i^ 

44i2 

46io 

48o7 

5oo5 

55 

4 

999° 

.160 

.33o 

.600 

.669 

.839 

55 

5 

620: 

54oo 

5598 

5795 

6992 

6189 

54 

5 

9.091008 

1178 

1  347 

i5i6 

1686 

i855 

54 

6 

6386 

6583 

6780 

6977 

7174 

7370 

53 

6 

2024 

2I93 

2362 

253o 

2699 

2868 

53 

7 

7667 

7763 

796o8i56 

8352 

8548 

52 

7 

3o37 

3206 

3374 

3542 

37n 

3879 

52 

8 

8744 

894o 

9i36|9332 

9527 

9723 

61 

8 

4047 

4216 

4384 

4552 

4720 

4888 

61 

9 

9918 

.114 

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.699 

•  894 

5o 

9 

5o56 

5223 

539i 

5559 

5726 

5894 

5o 

10 

9.031089 

1284 

1479 

i673 

186^2062 

49 

10 

6062 

6229 

6396 

6564 

673i 

6898 

49 

ii 

2267 

2461 

2646 

2839 

3o3J 

3227 

48 

H 

7066 

7232 

7399 

7666 

7733 

•7900 

43 

12 

342i 

36i5 

3809 

4002 

4i96 

4389 

47 

12 

8066 

8233 

8399 

8566 

8732 

8899 

47 

i3 

4582 

4776 

4969 

6162 

53555548 

46 

i3 

9066 

923l 

9398 

9564 

973o 

9896 

46 

i4 

574i 

5933 

6126 

63i9 

65i  116703 

45 

i4 

9.  100062 

0227 

o393 

0669 

0726 

0890 

45 

16 

6896 

7088 

7280  7472 

7664  7856 

44 

16 

1066 

1221 

1387 

1662 

1717 

i883 

44 

16 

8o48 

8239 

843i 

8623 

88i4 

9oo5 

43 

16 

2048 

2213 

2378 

2543 

2708 

2873 

43 

i7 

9197 

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17 

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32O2 

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42 

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21 

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2378 

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28 

3774 

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29 

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29 

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3o 

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28 

3i 

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6816 

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32 

6071 

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6806 

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27 

32 

76i3 

7772 

793i 

8090 

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27 

33 

7172 

7356 

7539 

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26 

33 

8667 

8726 

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26 

34 

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25 

34 

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25 

35 

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24 

35 

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1269 

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36  9.060460 

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1  1  88 

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23 

36 

1417 

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1732 

1890 

2047 

2205 

23 

37 

1661 

1732 

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22 

37 

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22 

38 

2639 

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3362 

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38 

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6126 

6281 

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42 

6962 

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7320  7499 

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9544 

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1066 

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45 

9854 

.  .  .9 

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.3i8 

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.627 

i4 

46 

1242 

1420 

1697 

i774 

1961 

2128 

i3 

46 

9.130781 

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1244 

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1662 

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47 

23o6 

2482 

26692836 

3oi3 

3i9o 

12 

47 

1706 

1860 

20l4 

2168 

2322 

2476 

12 

48 

3366 

3543 

37193896 

4072 

4248 

II 

48 

263o 

2783 

2937 

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3244 

3398 

II 

49 

4424 

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4777 

4962 

6128 

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IO 

49 

355i 

37o4 

3858 

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4i64 

43i7 

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5o 

548o 

5656 

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6007 

6182 

6358 

9 

5o 

4470 

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4929 

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9 

61 

6533 

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6883 

7068 

7233 

74o8 

8 

Si 

5387 

554o 

5693 

5845 

6998 

6160 

8 

62 

7583 

7758 

7933 

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8282 

8457 

7 

62 

63o3 

6455 

6607 

676.)  69i2 

7o64 

7 

53 

863i 

8806 

8980 

9164 

9328 

95o2 

6 

53 

7216 

7368 

7620 

76727824 

7976 

6 

54 

9676 

985o 

..24 

.108 

.372 

.545 

5 

54 

8128 

8279 

843i 

86828734 

8886 

5 

55 

9.080719 

o892 

1  0*6  6 

1239 

i4i3 

1686 

4 

55 

9o37 

9i88 

934o 

94919643 

9793 

4 

56 

1769 

I932 

2106 

227812461 

2624 

3 

56 

9944  .  .96 

.247 

.398  .548 

.699 

3 

57 

2797 

2969 

3  1  42 

33i4 

3487 

3659 

2 

57 

9.140860  looi 

n5i 

i3o2  i453 

i6o3 

2 

58 

3832 

4oo4 

4176 

4348 

4620 

4692 

I 

58 

175411904 

2066 

2206  2355  2606 

1 

69 

4864 

5o36 

6208 

538o 

555i 

6723 

O 

59 

2655  28o6'2956  3io6  3256  34o5 

O 

60" 

50" 

40" 

30" 

20" 

10" 

E 

60"     50"   40"  |  30"   20"  i  10"    . 

Co-sine  of  83 

Degrees. 

§ 

Co-sine  of  82  Degrees.     a 

_     <  1"  2"  3"  4"  5"  6"  7"  8'  9" 

p  p  .<  1"  2"  3"  4"  5"  6"  7"  S"  9'' 

irt{  18  37  55  74  92  111  129  148  166 

"{  16  32  48  64  80  96  112  128  144 

LOGARITHMIC    TANGENTS. 


.5 

Tangent  of  6  Degrees. 

.a 

Tangent  of  7  Degrees. 

m 

0" 

10"  |  20"  j  30" 

40" 

50" 

s 

0" 

10" 

20" 

30" 

40" 

50" 

o 

9  .021620 

I823J2O25 

2227 

2430 

263a 

59 

o 

9.o89i44 

9318 

9492 

9666 

9839 

..i3 

59 

i 

2834 

3o36  3238  3439 

364i 

3843 

58 

i 

9.o9oi87 

o36i 

o534 

0708 

0881 

io54 

58 

2 

4o44 

424514447 

4648 

4849 

5o5o 

57 

2 

1228 

i4oi 

i574 

I747 

I92O 

2093 

57 

3 

525i 

5452  5653 

5853 

6o54 

6254 

56 

3 

2266 

2439 

2612 

2784 

2957 

3129 

56 

4 

6465 

66556855 

7o55 

7255 

7455 

55 

4 

33o2 

3474  3647 

38ic; 

399i 

4i63 

55 

5 

7655 

78558o55 

8254 

8454 

8653 

54 

5 

4336 

45o8 

468o 

485i 

5o23 

5i95 

54 

6 

8852 

9o52  925i 

945o 

9649 

9848 

53 

6 

5367 

5538 

5710 

588i 

6o53 

6224 

53 

7 

9.o3oo46 

0245 

o444 

o64a  0841 

io39 

52 

7 

6395 

6567 

6738 

6909 

7080 

725i 

52 

8 

i23y 

i435 

i633 

i83i 

2029 

2227 

5i 

8 

7422 

7593 

7764 

7934 

8io5 

8276 

5i 

9 

2425 

2623 

2820 

3017 

32i5 

3412 

5o 

9 

8446 

8616 

8787 

8957 

9I27 

9298 

5o 

10 

3609 

38o6 

4oo3 

4200 

4397 

4594 

49 

10 

9468 

9638 

98o8 

9978 

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49 

1  1 

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4987 

5i84 

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5576 

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48 

ii 

9.  100487 

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0827 

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48 

12 

5969 

6i65 

636i 

6557 

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6948 

47 

12 

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2012 

2181 

235o 

47 

i3 

7i44 

7339 

7535 

773o 

7926 

8121 

46 

i3 

25l9 

2688 

2807 

3026 

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46 

i4 

83i6 

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87o6 

8901 

9095 

9290 

45 

i4 

3532 

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3869 

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45 

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9485 

9679 

9874 

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44 

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4542 

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16 

9  .  o4o65i 

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1039 

1232 

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43 

16 

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43 

17 

i8i3 

2007 

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2394 

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42 

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6556 

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7o58 

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4a 

18 

2973 

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18 

7559 

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4i 

19 

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20 

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6243 

39 

20 

9559 

9726 

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.224 

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39 

21 

6434 

6626 

6817 

7009 

7200 

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38 

21 

9.no556 

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38 

22 

7582 

7773 

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8:55 

8346 

8536 

37 

22 

i55i 

I7i6 

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2047 

2213 

2378 

37 

23 

8727 

8917 

9108 

9298 

9489 

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36 

23 

2543 

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2873 

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3368 

36 

24 

9869 

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35 

24 

3533 

3698 

3863 

4028 

4l92 

4357 

35 

25 

9.o5ioo8 

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1576 

1766 

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34 

25 

452i 

4686 

485o 

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34 

26 

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2333 

2522 

2711 

2900 

3o88 

33 

26 

55o7 

567i 

5835 

5999 

6i63 

6327 

33 

27 

3277 

3466 

3654 

3843 

4o3i 

42I9 

32 

27 

649i 

6655 

6818 

6982 

7i45 

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28 

4407 

4596 

4784 

4972 

5i59 

5347 

3i 

28 

7472 

7636 

7799 

7962 

8126 

8289j3i 

29 

5535 

6723 

5910 

6098 

6285 

6472 

3o 

29 

8452 

86i5 

8778 

8941 

9104 

9266 

3o 

3o 

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6847 

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7221 

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7594 

29 

3o 

9429 

9592 

9754 

9917 

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29 

3i 

7781 

7968 

8i55 

834i 

8528 

87i4 

28 

3i 

9.120404 

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0729 

0891 

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I2l5 

28 

32 

8900 

9086 

9273 

9459 

9645 

983i 

27 

32 

i377 

i539 

I7OI 

i863 

2O25 

2l87  27 

33 

9.060016 

O2O2 

o388 

0573 

o759 

o944 

26 

33 

2348 

25lO 

267I 

2833 

2994 

3i5626 

34 

n3o 

i3i5 

i5oo 

i685 

1870  2o55 

25 

34 

33i7 

3478 

364o 

38oi 

3962 

4123125 

35 

2240 

2425 

2610 

2795 

2979 

3i64 

24 

35 

4284 

4445 

46o6 

4766 

4927 

5o88 

24 

36 

3348 

3533 

37i7 

39oi 

4o85 

4269 

23 

36 

5249 

54o9 

557o 

573o 

589i 

6o5i 

23 

3? 

4453 

4637 

4821 

5oo5 

5i88|5372 

22 

3? 

6211 

6371 

6532 

6692 

6852 

7OI2 

22 

38 

5556 

5739 

5922 

6106 

69896478 

21 

38 

7I72 

7332 

7492 

765i 

7811 

797i 

21 

39 

6655 

6838 

7021 

7204 

73877670 

20 

39 

8i3o 

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8449 

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8768 

8928 

2O 

4o 

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8482  8664 

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4o 

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9246 

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9564 

9723 

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4i 

8846 

9029 

9211 

9393 

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18 

4i 

9.  i3oo4i 

0200 

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18 

42 

9938 

.  I2O 

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.483 

.664 

.846 

*7 

42 

0994 

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i3n 

1469 

1628 

i786 

*7 

43 

9.071027 

1208 

i389 

1570 

i75i 

I932 

16 

43 

1944 

2102 

2261 

2419 

2577 

2735 

16 

44 

2Il3 

2294 

2475 

2655 

2836 

3oi6 

i5 

44 

2893 

3o5o 

3208 

3366 

3524 

368i 

i5 

45 

3i97 

3377 

3558 

3738 

39i8 

4o98 

i4 

45 

383g 

3997 

4i54 

4312 

4469 

4626 

i4 

46 

4278 

4458 

4638 

48i7 

4997 

5i77 

i3 

46 

4784 

494i 

5o98 

5255 

5412 

5569 

i3 

4? 

5356 

5536 

57i5 

5895 

6o74'6253 

12 

47 

5726 

5883 

6o4o 

6i97 

6353 

65io 

12 

48 

6432 

6611 

679o 

6969 

7i48  7327 

II 

48 

6667 

6823 

698o 

7i36 

7292 

7449 

II 

49 

75o5 

7684 

7862 

8o4i 

82i98398 

10 

49 

76o5 

7761 

79i8 

8o74 

8230 

8386 

10 

5o 

8576 

8754 

8932 

9no 

9288 

9466 

9 

5o 

854a 

8698 

8854 

9009 

9i65 

932I 

9 

5i 

9644 

9822 

.... 

.177 

.355 

.532 

8 

5i 

9476 

9632 

9788 

9943 

..98 

.254 

8 

52 

9.080710 

o887 

1064 

1241 

i4i9 

i596 

7 

52 

9.140409 

o564 

0720 

0875 

io3o 

n85 

7 

53 

1773 

i95o 

2126 

23o3 

2480  2657 

6 

53 

i34o 

i495 

i65o 

i8o5 

i959 

2Il4 

6 

54 

2833 

3oio 

3i86 

3362 

3539 

37r5 

5 

54 

2269 

2424 

2578 

2733 

2887 

3o42 

5 

55 

389i 

4067 

4243 

44i9 

4595 

477i 

4 

55 

3196 

335o 

35o4 

3659 

38i3 

3967 

4 

56 

4947 

5l22 

5298 

5473 

5649 

5824 

3 

56 

4l2I 

4275 

4429 

4583 

4737 

4890 

3 

57 
58 

6000 
7o5o 

6i75 

7225 

635o 
74oo 

6525 
7574 

67oo6875 

7749|7924 

2 

I 

57 

58 

5o44 
5966 

5i98 
61  19 

535i 
6272 

55o5 
6425 

5659 
6579 

58i2 

6732 

2 
I 

59 

8098 

8273 

8447 

8621 

8795 

897o 

O 

59 

6885 

7o38 

7191 

7344 

7497 

765o 

O 

60" 

50" 

40" 

30" 

20" 

10" 

rj 

60" 

50"   40" 

30"  j  20" 

10" 

A 

Co-tangent  of  83  Degrees. 

.y 

§ 

Co-tangent  of  82  Degrees. 

i 

P  P«rt5  l"  2"  3//  4"  5"   6//   7"   8"   9" 

p  p  .<!"  2"  3"  4"  5"  6"  7"  8"  9" 

irc*  19  37  56  75  94  112  131  150  168 

trt{  16  33  49  65  81  98  114  130  146 

LOGARITHMIC 


i 

Sine  of  8  Degrees. 

A 

Sine  of  9  Degrees. 

i 

0-    |  10"   20" 

30" 

40"  |  50* 

s 

0"    |  10" 

20" 

30" 

40" 

50" 

o 

9.  M3555  37o5J3855 

4oo5 

4i54 

43o4 

59 

0 

9.194332 

4465 

4598 

473i 

4864 

4997 

59 

I 

4453  46o3  4-762 

4902 

5o5i 

6200 

58 

I 

6129 

6262 

5395 

5527 

566o 

5?92 

58 

3 

5349  5498  5648 

6797 

5g46  6096 

67 

2 

6926 

6067 

6189 

6322 

6454 

6586 

57 

3 

6243,6392  654i 

6690 

68396987 

56 

3 

6719 

685i 

6983 

7n5 

7247 

7379 

56 

4 

7i36  -7284  7433 

7681 

77307878 

55 

4 

7643 

-7776 

79°7 

8o38 

8i7o 

55 

5 

8026)8174 

83238471 

8619)876764 

5 

83o2 

8434 

8565 

8697 

8828 

896o 

54 

6 

89169063 

9211 

9358 

9606 

9654 

53 

6 

9091 

9223 

9354 

9486 

96i7 

9748 

53 

7 

980219949 

••97 

.244 

.392 

.539 

62 

7 

9879 

.  .11 

.142 

.273 

•  4o4 

.535 

62 

8 

9.1606860834 

0981 

1128 

1276 

l422 

61 

8 

9.200666 

0797 

0928 

1069 

n89 

1320 

5i 

9 

i569 

1716 

i863  2010 

2i57J23o4 

5o 

9 

i45i 

1682 

1712 

i843|i973 

2104 

5o 

10 
ii 

333o 

2597 

3476 

2744 
3623 

2891 
3769 

3o37|3i84 
39164061 

49 
48 

10 

ii 

2234 

3017 

2365 
3x4? 

2496 
3277 

2626 
34o7 

2-766 
3537 

2886 

3667 

49 

48 

12 

4208 

4354 

45oo4646 

4792)4g38 

47 

12 

3797 

3927 

4o57 

4i87 

43i7 

4447 

47 

i3 

5o83 

5229 

5375 

552i 

5666 

6812 

46 

i3 

4577 

4706 

4836 

4966 

5o95 

5225 

46 

i4 

5957 

6io3 

6248  6394 

6539 

6684 

45 

i4 

5354 

5484 

56i3 

5743 

5872 

6002 

45 

i5 

683o 

6975 

7120  7265 

74io 

7555 

44 

i5 

6i3i 

6260 

6389 

65i9 

6648 

6777 

44 

16 

7700 

7845 

7990  8  1  35 

82?9 

8424 

43 

16 

69o6 

7o35 

7i64 

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17 

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8858  9.002 

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18 

9435 

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9-7249868 

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21 

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22 

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32 

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27 

32 

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33 

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26 

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34 

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34 

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1242 

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35 

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35 

1367 

1492 

1616 

1741 

1866 

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24 

36 

4744 

4883 

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23 

36 

2116 

2239 

2364 

2488 

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2737 

23 

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5579 

57i7 

5856  6996 

6i34 

6273 

22 

37 

2861 

2986 

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3234 

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38 

64i  . 

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6688  6827  6966 

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21 

38 

36ob 

373o 

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.i39 

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ll 

42 

6573 

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68i9 

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7i88 

17 

A3 

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0826  0963 

1  100 

1237 

16 

43 

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7434 

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4*1'   1374 

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45    2196 

2333 

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2743 

2870 

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45 

8784 

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46 

3oi6 

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3562 

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46 

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47 

3834 

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12 

47 

9.  230262 

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12 

48 

465i 

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II 

48 

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1228 

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II 

49 

5466 

56o2 

5738 

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6009 

6i45 

10 

49 

1716 

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2079 

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2323 

10 

5o    6280 

64i6 

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6822 

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9 

5o 

2444 

2565 

268-7 

2808 

293o 

3o5i 

9 

Si 

•»O02 

7228 

7363 

7498 

7633 

7768 

8 

61 

3172 

3293 

34i5 

3536 

3657 

3778 

8 

52      '.qo3 

53    fr-tfi 

8o38 
8847 

8173 
8981 

83o8  8442 
9n6  9260 

8677 
9385 

7 
6 

52 

53 

3899 
4626 

4O20 

4746 

4i4i 
4867 

4262 
4987 

4383 
6108 

45o4 

6 

54    96*9 

9654 

9788 

9923 

..57 

.191 

5 

54 

5349 

547o 

559i 

6711 

5832 

6962 

5 

55  9.1903-^5 
56    n3o 

o46o 
1264 

0694 

0728 
i532 

0862 
1666 

0996 
1799 

4 
3 

55 
56 

6073 
6796 

6i93 
6916 

63i3 
7o35 

6434 
7i55 

6554 

7275 

6674 
7395 

4 
3 

67 

I933 

2066 

22OO 

2334  2467 

A 

2601 

2 

57 

75i5 

7635 

7755 

7875 

7995 

8n5 

2 

58 

2734 

2868 

3001 

3i34i3268 

34oi 

I 

58 

8235 

8355 

8474 

8594 

87i4 

8834 

I 

59    3534 

3667 

38oo 

39334066 

4199 

O 

59 

8963 

9o739i92 

93l2 

943i 

955i 

0 

60" 

50" 

40" 

30" 

20" 

10" 

d 

60" 

50"   40" 

30"  |  20" 

10" 

^ 

Co-sine  of  81 

Degrees. 

9 

Co-sine  of  80  Degrees. 

8 

(  \"  2"  3"  4"  5"  6"  7"  8"  9" 

P  P  f  fl"  2//  3//  4//  5"  6"  7"  8"  9" 

P.  Part  J  H  2g  42  5fi  7Q  85  9g  H3  12? 

irt\  13  25  38  50  63  75  88  101  113 

LOGARITHMIC    TANGENTS. 


33 


d 

Tangont  of  8  Degrees. 

.s 

Tangent  of  9  Degrees. 

ii 

0" 

10" 

20" 

30" 

40" 

50" 

2 

0" 

10" 

20" 

30" 

40" 

50" 

0 

9.147803 

7955 

8108 

8261 

84i3 

8566 

59 

o 

9.199713 

9849 

9985 

.  121 

.257 

.393 

59 

I 

8718 

8871 

9023 

9!75 

9328 

948o 

58 

i 

9.200529 

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0801 

o937 

io73 

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58 

2 

9632 

9784 

9936 

.88 

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57 

2 

1  345 

i48i 

1616 

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1888 

2022 

$7 

3 

9.i5o544 

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56 

3 

2i5g 

2294 

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2565 

2701 

2836 

56 

4 

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1606 

I757 

1909 

2060 

2211 

55 

4 

2971 

3107 

3242 

3377 

35i2 

3647 

55 

5 

2363 

25i4 

2665 

2816 

2967 

3u8 

54 

5 

3782 

39i8 

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4x88 

4322 

4457 

54 

6 

3269 

3420 

357i 

3722 

3873 

4023 

53 

6 

4592 

4727 

4862 

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5266 

53 

7 

4i74 

4325 

4475 

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7 

54oo 

5535 

5669 

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52 

8 

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5828 

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8 

620-7 

6342 

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6744 

6878 

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9 

5978 

6128 

6278 

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6578 

6728 

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9 

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10 

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49 

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49 

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48 

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48 

12 

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12 

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47 

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16 

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18 

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20 

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39 

20 

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21 

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23 

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36 

23 

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24 

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35 

24 

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25 

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25 

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9840 

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34 

26 

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26 

9.220492 

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33 

27 

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2478 

2623 

32 

27 

1272 

1402 

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1662 

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1922 

32 

28 

2767 

2912 

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3345 

3489 

3i 

28 

2OJ>2 

2l82 

23ll 

244i 

2571 

2700 

3i 

29 

3634 

3778 

3922 

4o67 

4211 

4355 

3o 

29 

283o 

2060 

3o89 

32i8 

3348 

3477 

3o 

3o 

4499 

4643 

4787 

493i 

5075 

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29 

3o 

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3736 

3865 

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4253 

2  9. 

3i 

5362 

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565o 

5793 

5937 

6080 

28 

3i 

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464o 

4769 

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28 

32 

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6367 

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6654 

6797 

6941 

27 

32 

5i56 

5285 

54i4 

5543 

5671 

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27 

33 

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7227 

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7800 

26 

33 

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6o58 

6186 

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26 

34 

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25 

34 

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6829 

6957 

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25 

35 

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24 

35 

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24 

36 

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37 

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17 

42 

2826 

2953 

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3206 

3333 

346o 

17 

43 

5597 

5737 

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6299 

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43 

3586 

3713 

3839 

3966 

4092 

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16 

44 

6439 

6579 

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6860 

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7140 

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44 

4345 

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4598 

4724 

485o 

4976 

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45 

7280 

7420 

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7700 

7840 

7980 

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45 

5io3 

5229 

5355 

548i 

5607 

5733 

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46 

8120 

8259 

8399 

8539 

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8818 

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46 

5859 

5985 

61  ii 

6237 

6362 

6488 

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47 

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9097 

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12 

47 

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6865 

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7117 

7242 

12 

48 

9794 

9933 

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II 

48 

7368 

7493 

7619 

7744 

7870 

7995 

II 

49 

9.  190629 

0768 

0907 

io46 

1184 

i323 

IO 

49 

8120 

8246 

837i 

8496 

8621 

8747 

IO 

5o 

1462 

1  60  1 

i739 

1878 

2017 

2i55 

9 

5o 

8872 

8997 

9I22 

9247 

9372 

9497 

9 

5i 

2294 

2432 

257I 

2709 

2848 

2986 

8 

5i 

9622 

974? 

9872 

9996 

.  121 

.246 

8 

52 

3l24 

3262 

34oi 

3539 

3677 

38i5 

7 

52 

9.24o37i 

0495 

062O 

o745 

o869 

o994 

7 

53 

3953 

4091 

4229 

4367 

45o5 

4642 

6 

53 

1118 

1243 

i367 

l492 

1616 

1741 

6 

54 

4780 

4918 

5o56 

5ig3 

533i 

5468 

5 

54 

i8f5 

1989 

2114 

2238 

2362 

2486 

5 

55 

56o6 

5743 

588i 

6018 

6i56 

6293 

4 

55 

26^0 

2734 

2858 

2982 

3io6 

323o 

4 

56 

643o 

6567 

6705 

6842 

6979 

7116 

3 

56 

3354 

3478 

36o2 

3726 

385o 

3974 

3 

57 

7253 

739° 

75.27 

7664 

7801 

7938 

2 

57 

4097 

4221 

4345 

4468 

4592 

4?i5 

a 

58 

8o74 

8211 

8348 

8484 

8621 

8758 

I 

58 

4839 

4962 

5o86 

52O9 

5333 

5456 

i 

59 

8894 

go3i 

9167 

93o4 

944o 

9576 

O 

59 

5579 

5703 

5826 

5949 

6072 

6i96 

o 

60" 

50" 

40" 

30" 

20" 

10" 

a 

60" 

50" 

40" 

30" 

20" 

10" 

d 

Co-tangent  of  81  Degrees. 

§ 

Co-tangent  of  80  Degrees. 

1 

P  P  f<l"  2"  3"  4"  5"  6"  7"  8"  9" 

.5  1"  2"  3"  4"  5"  6"  7"  8"  9" 

1  14  29  43  58  72  86  101  115  130 

in\  13  26  39  52  65  7$  91  103  116 

LOGARITHMIC    SINES. 


.5 

Sine  of  10  Degrees. 

O 

Sine  of  1  1  Degrees. 

m 

0"    |  10"  |  207 

30" 

40"   5(X 

2 

0"     10"  |  20" 

30" 

40" 

50" 

0 

9.23967o!979o|99o9 

..28 

.i48|.267 

59 

0 

9.280599  O?O7 

o8i5 

O924 

1032 

u4o 

59 

i 

9.24o386 

o5o5io624 

o744 

o863 

0982 

58 

I 

1248  i356 

i465 

i573 

1681 

i789 

58 

2 

I  IOI 

1220  i339 

i458 

i576 

i695 

57 

2 

189-7  2oo5 

2Il3 

222O 

2328 

2436 

57 

3 

1814  I933'2o52 

2170 

2289 

2408 

56 

3 

2544  2652 

2760 

2867 

2975 

3o83 

56 

4 

252626452763 

2882 

3  oo  i 

3lIQ 

55 

4 

31903298 

34o6 

35i3 

362i 

3728 

55 

5 

3237 

3356 

3474 

3592 

37u 

382q 

54 

5 

3836 

3943 

4o5i 

4i58 

4266 

4373 

54 

6 

3947 

4o65 

4i84 

43o2 

4420 

4538 

53 

6 

448o 

4588 

4695 

4802 

49o9 

5oi7 

53 

7 

4656 

4774 

4892 

5oio 

5i28 

5245 

52 

7 

5i24 

523i 

5338 

5445 

5552 

5659 

52 

8 

5363 

548i 

5599 

6717 

5834 

5952 

5  1 

8 

5766 

5873 

598o 

6087 

6i94 

63oi 

5i 

9 

6069 

6187 

63o5 

6422 

654o 

6657 

5o 

9 

64o8 

65i4 

6621 

6-728 

6835 

694i 

5o 

10 

6775 

6892 

7oo9 

7127 

7244 

736i 

49 

10 

7o48 

7i55 

-7261 

7368 

7474 

758i 

49 

ii 

7478 

7596 

77i3 

7830 

7947 

8o64  48 

1  1 

•7688 

7794 

79oo 

8007 

8n3 

8220 

48 

12 

8181 

8298 

84i5 

8532 

8649 

8766 

47 

12 

8326 

8432 

8539 

8645 

875i 

8857 

47 

i3 

8883 

8999 

9116 

9233 

935o 

9466 

46 

i3 

8964 

9o7o 

9i76 

9282 

9388 

9494 

46 

i4 

9583 

97oo 

98169933 

..49 

.166 

45 

i4 

9600 

97o6 

9812 

99i8 

..24 

.i3o 

45 

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9.250282 

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44 

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9.290236 

0342 

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o765 

44 

16 

0980 

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I2l3 

1329 

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i56i 

43 

16 

08-70 

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1082 

1187 

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i398 

43 

17 

1677 

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1909 

2026 

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2257 

42 

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1610 

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1820 

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2031 

42 

18 

2373 

2489 

26o5 

2720 

2836 

2952 

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18 

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2242 

2347 

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3:83 

3299 

34i4 

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2768 

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29-79 

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20 

376i 

3876 

3992  4io7 

4223 

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39 

20 

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38 

21 

4029 

4i34 

4239 

4344 

4448 

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38 

22    5i44 

5259 

5374 

5490 

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37 

22 

4658 

4763 

4867 

4972 

5o77 

5i8i 

37 

28    5834 

5949 

6064 

6179 

6294  64o9 

36 

23 

5286 

539i 

5495 

56oo 

57o4 

58o9 

36 

24 

6523 

6638 

6753 

6867 

6982i7o96 

35 

24 

5913 

60  1  7 

6122 

6226 

633o 

6435 

35 

25    7211 

7326 

744o  7554 

7669 

7783 

34 

25 

6539 

6643 

6747 

6852 

6956 

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34 

26   7898 

8012 

81268241 

8355 

8469 

33 

26 

7164 

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33 

27    8583 

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32 

27 

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7892 

7996 

8100 

8204 

83o8 

32 

28!    9268 

9382 

9495  9609 

9723 

9837 

3i 

28 

8412 

85i5 

86i9 

8?23 

8827 

893o 

Si 

29    995i 

..65 

.178 

.292 

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.5i9 

3o 

29 

9o34 

9i38 

924i 

9345 

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9552 

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So'g.  26o633 

0747 

0860  0974 

io87 

I2OI 

29 

3o 

9655 

9759 

9862 

9966 

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29 

3i 

i3i4 

1428 

i54i 

i654 

i768 

1881 

28 

3i 

9.300276 

o379 

0482 

o586 

o689 

0792 

28 

32 

I994 

2107 

222O 

2334 

2447 

256o 

27 

32 

o895 

0999 

1  102 

I2O5 

i3o* 

i4i  i 

27 

33 

2673 

2786 

2899 

3012 

3i25 

3238 

26 

33 

i5i4 

1617 

I72O 

1823 

I926 

2O29 

26 

34 

335i 

3464 

3576 

3689 

3802- 

39i5 

25 

34 

2l32 

2235 

2337 

2440 

2543 

2646 

25 

35 

4027 

4i4o 

42534365 

4478 

4590 

24 

35 

2748 

285i 

2954 

3o57 

3i59 

3262 

24 

36 

47o3 

48i5 

4928  5o4o 

5i53 

5265 

23 

36 

3364 

3467 

3569 

3672 

3774 

3877 

23 

37 

5377 

5490 

56o2 

57i45827 

5939 

22 

37 

3979 

4082 

4i84 

428-7 

4389 

449i 

22 

38 

6o5i 

6i63 

6275  6387 

6499 

66n 

21 

38 

4593 

4696 

4798 

49oo;5oo2 

5io4 

21 

39 

6723 

6835 

6947-7059 

7i7i 

7283 

2O 

39 

52O7 

53o9 

54n 

55i3;56i5 

57i7 

2O 

4o 

7395 

75o6 

7618 

773o 

784i 

7953 

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4o 

58i9 

5921 

6023 

6i25  6227 

6328 

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4i 

8o65 

8176 

8288  8399 

85n 

8622 

18 

4i 

643o 

6532 

6634 

67366837 

6939 

18 

42 

8734 

8845 

89579068 

91-79 

9291 

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42 

7o4i 

7142 

7244 

7346'7447 

7549 

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43 

9402 

95i3 

96249736 

9847 

9958 

16 

43 

765o 

7752 

7853 

7955 

8o56 

8r58 

16 

44 

9.27oo69 

0180 

0291 

0402 

o5i3 

0624 

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44 

8259 

836o 

8462 

8563 

8664 

8766 

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45 
46 

o735 
i4oo 

o846 
i5io 

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1621 

io67 

I732 

1178 
1842 

1289 
i953 

i4 
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45 
46 

8867 
9474 

8968 
9575 

9o69 
9676 

91709272 
9777  9878 

9373 
9979 

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4? 

2064 

2174 

2285 

23g5  25o5 

2616* 

12 

4? 

9.  3  i  0080 

0181 

0282 

o382 

o483 

o584 

12 

48 

2726 

2837 

2947 

3o573i68 

3278 

I  I 

48 

o685 

0786 

0886 

0987 

1088 

n89 

II 

49 
5o 

3388 
4049 

3498 
4i59 

36o8  37i8  3829 
4269  4379'4489 

3939 

4598 

IO 

9 

49 

5o 

I289 

i893 

i39o 
i993 

i49o 

2094 

i59i 
2194 

l692 
2294 

I792 

2395 

10 

5i 

4708 

4818 

49285o38|5i48 

5257 

8 

5i 

2495 

2595 

2696 

2796 

2896 

2997 

8 

52 

5367 

5477 

5586 

5696 

58o5 

59i5 

7 

5'2 

3o97 

3i97 

3297 

3397  3497 

3597 

7 

53 

6o25 

6i34 

6s43 

6353 

6462 

6572 

6 

53 

3698 

3798 

3898 

3998j4o98 

4i98 

6 

54 

6681 

679o 

6900 

•7009 

7118 

7227 

5 

54 

4297 

4397 

4497 

4597^697 

4797 

5 

55 

7337 

7446 

7555 

7664 

7773 

7882 

4 

55 

4897 

4996 

5o96 

5i96  5295 

5395 

4 

56 

•7991 

8100 

8209 

83i8 

8427 

8536 

3 

56 

5495 

5594 

5694 

5793,5893 

5993 

3 

*7 

58 

86458753 

9297  9406 

8862 
95i4 

897i 
9623 

9080 
973i 

9i88 
984o 

2 
I 

57 
58 

6o92 
6689 

6i92 

6788 

62^1 

6887 

639o649o6589 
608670867185 

2 
I 

59 

9948 

.  .57 

.i65 

•274 

.382 

•  49i 

o 

59 

•7284 

7383 

7482 

7582  7681  7780 

O 

60" 

50" 

40" 

30" 

20" 

10" 

B 

60"     50"  |  40" 

30"   20"  I  10" 

. 

Co-sine  of  79 

Degrees. 

.££ 

~. 

Co-sine  of  78  Degrees 

1 

A  I"  .2"  3"  4" 

5"  6"  7"  8"  9" 

P  P  tf  1"  2"  3"  4"  5"  6"  7"  8"  9" 

r'PartJ  11  23  34  45 

57  68  80  91  102 

m\  10  21  31  41  32  62  72  83  93 

LOGARITHMIC    TANGENTS. 


fl. 

Tangent  of  10  Degrees. 

a 

Tangent  of  1  1  Degrees. 

9 

0" 

10" 

20" 

30" 

40" 

50" 

•• 

0" 

10" 

20" 

30" 

40" 

50" 

o 

9.2463i9 

5442 

6565 

6688 

6811 

6934 

59 

0 

9.288652 

8765 

38?7 

8989 

9IO2 

92l4 

9 

i 

7°57 

7i8o 

73o3 

7426 

7548 

767i 

58 

I 

9326 

9438 

9663 

9775 

9887 

8 

2 

7794 

79i7 

8o39 

8162 

8285 

84o7 

57 

2 

9999 

in 

223 

335 

447 

559 

7 

3 

853o 

8652 

8775 

8897 

9020 

9l42 

56 

3 

9.290671 

o783 

o895 

1007 

n9 

23l 

6 

4 

9264 

9387 

95o9 

963i 

9753 

;876 

55 

4 

1  342 

454 

566 

678 

789 

9oi 

5 

5 

9998 

120 

.242 

364 

.486 

608 

54 

5 

20l3 

2124 

2236 

2347 

570 

4 

6 

9.250730 

o852 

o974 

1096 

1218 

i339 

53 

6 

2682 

2793 

29o5 

3oi6 

;I27 

239 

3 

7 

i46i 

583 

I7o5 

1826 

i948 

2O70 

52 

7 

335o 

346i 

572 

3684 

906 

2 

8 

2I9I 

23i3 

2434 

2556 

2677 

2799 

5i 

8 

4017 

4128 

239 

435i 

462 

4573 

I 

9 

2920 

>o4i 

3i63 

3284 

34o5 

3527 

5o. 

9 

4684 

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5oi6 

5l27 

238 

O 

10 

3648 

3769 

389o 

ion 

4i32 

4253 

49 

10 

5349 

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557i 

568i 

5792 

9c3 

9 

n 

4374 

4495 

46i6 

4737 

4858 

4979 

48 

n 

6oi3 

6124 

5235 

6345 

6456 

6566 

8 

12 

5  1  oo 

5221 

534i 

5462 

5583 

57o3 

47 

12 

6677 

6787 

6898 

7008 

7ii9 

7229 

7 

i3 

5824 

5945 

6o65 

6186 

63o6 

642  7 

46 

i3 

745o 

756o 

7670 

778i 

7891 

6 

i4 

654? 

6668 

6788 

6908 

7029 

7149 

45 

i4 

8001 

8111 

8221 

8332 

8442 

8552 

5 

i5 

7269 

7389 

75io 

763o 

775o 

7870 

44 

i5 

8662 

8772 

8882 

8992 

9102 

92I2 

4 

16 

799° 

8110 

823o 

835o 

847o 

859o 

43 

16 

9322 

943  1 

954i 

965i 

976i 

987I 

43 

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8710 

883o 

8950 

9069 

9i89 

93o9 

42 

17 

9980 

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200 

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4i9 

529 

2 

18 

9429 

9548 

9668 

9787 

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ii 

18 

9.3oo638 

0748 

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186 

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9.260146 

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4o 

19 

1295 

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i5i4 

1624 

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O 

20 

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39 

20 

1951 

2061 

2I70 

2279 

2388 

2497 

9 

21 

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697 

1816 

1935 

2o54 

2I?3 

38 

21 

2607 

2716 

2825 

2934 

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3i52 

8 

22 

2292 

2411 

253o 

2649 

2768 

2887 

37 

22 

3261 

3370 

3479 

3588 

3697 

38o5 

7 

23 

3oo5 

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3243 

336! 

348o 

3599 

36 

23 

39i4 

4i32 

424i 

4349 

4458 

36 

24 

37i7 

3836 

3954 

4o73 

4191 

43io 

35 

24 

4567 

4675 

4784 

4893 

5ooi 

5no 

35 

25 

4428 

4547 

4665 

4783 

4902 

5O2O 

34 

25 

52i8 

5327 

5435 

5544 

5652 

576i 

34 

26 

5i38 

5256 

5375 

5493 

56ii 

5729 

33 

26 

5869 

5977 

6086 

6i94 

63o2 

64io 

33 

27 

5847 

5965 

6o83 

6201 

6319 

6437 

32 

27 

65i9 

6627 

6735 

6843 

695i 

7o59 

32 

28 

6555 

6673 

679o 

6908 

7026 

7i44 

3i 

28 

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7276 

7384 

7492 

76oo 

7708 

i 

29 

7261 

7379 

7497 

7614 

7732 

7849 

3o 

29 

•7816 

7923 

8o3i 

8i39 

824-7 

8355 

lo 

3o 

7967 

8o84 

8202 

8319 

8437 

8554 

29 

3o 

8463 

8570 

8678 

8786 

8893 

9001 

29 

3i 

8671 

8789 

89o6 

9023 

9140 

9258 

28 

3i 

9109 

9216 

9324 

9432 

9539 

964? 

28 

32 

9375 

9492 

96o9 

9726 

9843 

996o 

27 

32 

9754 

9862 

9969 

..76 

.184 

.29I 

27 

33 

9,27oo77 

0194 

o3ii 

0428 

o545 

0662 

26 

33 

9.310399 

o5o6 

o6i3 

0720 

0828 

o935 

26 

34 

°779 

o895 

1012 

II29 

1246 

i362 

25 

34 

1042 

1x49 

1256 

i364 

i47i 

i578 

25 

35 

i479 

i595 

I7I2 

i829 

1945 

2062 

24 

35 

i685 

1792 

i899 

2006 

2113 

2220 

24 

36 

2I78 

2294 

2411 

2527 

2644 

276o 

23 

36 

2327 

2433 

254o 

2647 

2754 

286l 

23 

37 

2876 

2992 

3io9 

3225 

334i 

3457 

22 

37 

2968 

3o74 

3i8i 

3288 

3394 

35oi 

22 

38 

3573 

3689 

38o5 

392I 

4o37 

4i53 

21 

38 

36o8 

37i4 

382i 

3927 

4o34 

4i4o 

21 

39 

4269 

4385 

45oi 

4617 

4733 

4849 

2O 

39 

4247 

4353 

446o 

4566 

4672 

4779 

2O 

4o 

4g64 

5o8o 

5i96 

53i2 

5427 

5543 

I9 

4o 

4885 

4991 

5o98 

52o4 

53io 

54i6 

19 

4i 

5658 

5774 

589o 

6oo5 

6121 

6236 

1  8 

4i 

5523 

5629 

5735 

584i 

5947 

6o53 

18 

42 

635i 

6467 

6582 

6698 

68i3 

6928 

17 

42 

6i59 

6265 

637i 

6477 

6583 

6689 

17 

43 

7o43 

7i59 

7274 

7389 

75o4 

76i9 

16 

43 

6795 

6901 

7oo7 

7ii3 

72l8 

7324 

16 

44 

7734 

•7849 

7964 

819^ 

83o9 

i5 

44 

743o 

7536 

764i 

7747 

7853 

79^8 

i5 

45 

8424 

8539 

8654 

876c 

8884 

8998 

i4 

45 

8o64 

8170 

8275 

838i 

8486 

8592 

i4 

46 

9n3 

9228 

9342 

9457 

95-72 

9686 

i3 

46 

8697 

88o3 

89o8 

9oi3 

9ii9 

9224 

i3 

47 

9801 

99i5 

..3o 

•  i44 

.259 

.373 

12 

47 

933o 

9435 

954o 

9645 

975i 

9856 

12 

48 

9.280488 

0602 

07I7 

o83i 

o945 

io59 

II 

48 

9961 

..66 

.171 

.277 

.382 

.487 

II 

49 

n74 

1288 

1402 

i5i6 

i63o 

i74^ 

IO 

49 

9.320592 

0697 

0802 

o9O7 

IOI2 

1117 

10 

5o 

i858 

i973 

2087 

2201 

23l/ 

2428 

g 

5o 

1222 

1326 

i43i 

i536 

i64i 

1746 

9 

5i 

2542 

2656 

2770 

2884 

2998 

3iu 

8 

5i 

i85i 

i955 

2060 

2i65 

2269 

2374 

8 

52 

3225 

3339 

3453 

3566 

368o 

3793 

7 

52 

24-79 

2583 

2688 

2793 

2897 

3oo2 

7 

53 

39o7 

4021 

4i34 

4248 

436i 

4474 

6 

53 

3io6 

3211 

33i5 

3420 

3524 

3628 

6 

54 

4588 

47oi 

48i5 

4928 

5o4i 

5i54 

5 

54 

3733 

3837 

394i 

4o46 

4i5o 

4254 

5 

55 

5268 

538i 

549^ 

56o7 

572O 

5833 

4 

55 

4358 

4463 

4567 

4671 

4775 

4879 

4 

56 

5947 

6060 

617^ 

6286 

6399 

65i2 

3 

56 

4Q83 

5o87 

5i9i 

5295 

5399 

55o3 

3 

5? 

6624 

6737 

685o 

6963 

7o76 

7i89 

2 

57 

56o7 

57n 

58i5 

59i9 

6o23 

6127 

2 

58 

73oi 

74iJ 

7527 

7639 

7752 

7865 

I 

58 

623i 

6334 

6438 

6542 

6646 

6749 

I 

59 

7977 

8o9o 

8202 

83i5 

8427 

854o 

0 

59 

6853 

6957 

7060 

7i64 

•7267 

737 

O 

60" 

50" 

40" 

30" 

20" 

10" 

. 

60" 

50" 

40" 

30" 

20" 

10" 

d 

Co-tangent  of  79  Degrees. 

% 

Co-tangent  of  78  Degrees. 

i 

P  Port  5  l"  %"  3"  4"  5"   6"   7"   8"   9" 

(  1"  2"  3"  4"  5"  6"  7"  S"  9" 

irl\  12  23  35  47  59  70  82  94  106 

P.PartJn  22  32  43  54  65  75  86  97 

36 


LOGARITHMIC    SINES. 


Jj 

Sine  of  12  Degrees. 

«• 

Sine  of  13  Degrees. 

53 

0" 

10" 

20"   30"   40" 

50" 

* 

0" 

10" 

20" 

30" 

40" 

50" 

o 

9-3i7879 

797« 

8077:81768275 

8374 

i>9 

09.352088 

2179 

2270 

2362  2453 

2544 

59 

i 

8473 

8572 

867i  8769 

8868 

8967 

58 

I 

2635 

2-726 

28l? 

2908 

2999 

3o9o 

58 

2 

9o66 

9i65 

92639362 

946i 

57 

2 

3i8i 

3272 

3363 

3454 

3545 

3636 

57 

J 

9658 

9757 

9855 

9954 

..52 

9i5? 

56 

'. 

3726 

38i7 

39o8 

3999 

4o90 

4i8o 

56 

L 

9.320249 

o348 

o446 

o545 

o643 

0742 

55 

L 

427I 

4362 

4452 

4543 

4634 

4724 

55 

e 

o84o 

o938 

io37 

ii35 

1233 

i332 

54 

t 

48i5 

49o6 

4996 

5o87 

5i77 

5268 

54 

6 

i43o 

i528 

1626 

1-724 

1822 

I92I 

53 

6 

5358 

5449 

5539 

563o 

5720 

58io 

53 

7 

20I9 

2II7 

2215 

23i3 

2411 

25o9 

52 

7 

59oi 

599i 

6081 

6172 

6262 

6352 

52 

8 

26o7 

27o5 

28O2  29OO 

2998 

3o96 

5i 

8 

6443 

6533 

6623 

67i3 

68o3 

6894 

Si 

9 

3i94 

3292 

3389l3487 

3585 

3683 

5o 

9 

6984 

7074 

716^ 

7344 

7434 

5o 

10 

9.32378o 

3878 

39754o73 

4171 

4268 

49 

10 

9.357524 

76i4 

77°4 

7794 

7884 

7974 

49 

ii 

4366 

4463 

456i  4658 

4?56 

4853 

48 

ii 

8064 

8i54 

8243 

8333 

8423 

85i3 

48 

12 

495o 

5o48|5i45 

5243 

534o 

5437 

47 

12 

86o3 

8692 

8782 

8872 

8962 

9o5i 

47 

i: 

5534 

5632  5-729 

5826 

5923 

6020 

46 

i3 

9i4i 

923l 

9320 

94io 

9499 

9589 

46 

i4 

6ii7 

62i563i2 

64o9 

65o6 

66o3 

45 

ii 

9678 

9768 

9858 

9947 

..36 

.126 

45 

i5 

67oo 

6797  6894 

699i 

7o87 

7184 

44 

i5 

9.36o2i5 

o3o5 

o394 

o484 

o573 

0662 

44 

16 

•7281 

7378  7475 

7572 

-7668 

7765 

43 

16 

0752 

o84i 

o93o 

ioi9 

1109 

ii98 

43 

i7 

•7862 

7958  8o55 

8i52 

8248 

8345 

42 

17 

I287 

i376 

i465 

1  554 

1  644 

I733 

42 

18 

8442 

85388635 

873i 

8828 

8924 

4i 

18 

1822 

i9n 

2OOO 

2089 

2I78 

2267 

4i 

i9 

902I 

9II792l3 

93io 

94o6 

9502 

4o 

19 

2356 

2445 

2534 

2623 

27II 

28OO 

4o 

20 

9.329599 

9695  979i 

9888 

9984 

..80 

39 

20 

9.362889 

a978 

3o67 

3i56 

3244 

3333 

39 

21 

9.33oi76 

0272  o368 

o465 

o56i 

o657 

38 

21 

3422 

35n 

3599 

3688 

3777 

3865 

38 

22 

o753 

0849  °945 

io4i 

1187 

1233 

37 

22 

3954 

4042 

4i3i 

4220 

43o8 

4397 

37 

23 

i329 

l424  l520 

1616 

I7I2 

1808 

36 

23 

4485 

4574 

4662 

475i 

4839 

4927 

36 

24 

I9o3 

I999|2o95 

2I9I 

2286 

2382 

35 

24 

5oi6 

5io4 

5i93 

5281 

5369 

5457 

35 

25 

2478 

2573  2669 

2-764 

2860 

2956 

34 

25 

5546 

5634 

5722 

58io 

5899 

5987 

34 

26 

3o5i 

3i47 

3242 

3337 

3433 

3528 

33 

26 

6o75 

6i63 

625i 

6339 

642-7 

65i6 

33 

27 

3624 

37i9 

38i4 

39io 

4oo5 

4ioo 

32 

27 

66o4 

6692 

678o 

6868 

6956 

7o44 

32 

28 

4i95 

4291 

4386 

448  1 

4576 

467i 

3i 

28 

7i3i 

72I9 

73o7 

7395 

7483 

757i 

3i 

29 

4767 

4862 

4957 

5o52 

5i47 

5242 

3o 

29 

7659 

7747 

7834 

7922 

8010 

8098 

3o 

3o 

9.335337 

5432 

5527 

5622 

57i6 

58ii 

29 

3o 

9.368i85 

8273 

836i 

8448 

8536 

8624 

29 

3i 

59o6 

6001 

6o96 

6i9i 

6285 

638o 

28 

3i 

8711 

8799 

8886 

8974 

9o6i 

9i49 

28 

32 

6475 

657o 

6664 

6759 

6854 

6948 

27 

32 

9236 

94n 

9499 

9586 

9673 

27 

33 

?o43 

7l37  7232 

7326 

7421 

75i5 

26 

33 

9761 

9848 

9936 

..23 

.  no 

.i97 

26 

34 

76io 

77o4  7799 

7893 

7988 

8082 

25 

34 

9.370285 

o372 

o459 

o546 

o634 

072I 

25 

35 

81-76 

82-71  8365 

8459 

8553 

8648 

24 

35 

0808 

o895 

0982 

io69 

ii56 

1243 

24 

36 

8742 

8836893o 

9024 

9ii8 

92I2 

23 

36 

i33o 

1417 

i5o4 

i59i 

16-78 

i765 

23 

37 

93o7 

9401^495 

9589 

9683 

9777 

22 

37 

i852 

i939 

2026 

2113 

2200 

228-7 

22 

38 

9871 

9964  -.58 

.246 

.34o 

21 

38 

2373 

2460 

254-7 

2634 

272I  28o7 

21 

39 

9.  34o434 

05280621 

o7i5 

o8o9 

0903 

2O 

-39 

2894 

298i 

3o67 

3i54 

324i  3327 

2O 

4o 

9.340996 

1090  1184 

I27? 

i37i 

1  464 

'9 

4o 

9.3734i4 

35oo 

3587 

3674 

376o 

3847 

'9 

4i 

i558 

1  652  i745 

i839 

I932 

2026 

18 

4i 

3933 

4O20 

4io6 

4l92 

4279 

4365 

18 

42 

2119 

2212  23o6 

2399 

2493 

2586 

'7 

42 

4452 

4538 

4624 

47n 

4797 

4883 

17 

43 

2679 

2772  2866 

2959 

3o52 

3i45 

16 

43 

497o 

5o56 

5i42 

5228 

53i4 

54oi 

16 

44 

3239 

3332  3425 

35i8 

36ii 

3704 

i5 

44 

5487 

5573 

5659 

5745 

583i 

59i7 

i5 

45 

3797 

389o3983 

4o76 

4i69 

4262 

i4 

45 

6oo3 

6o89 

6i75 

6261 

6347 

6433 

i4 

46 

4355 

4448454i 

4634 

4727|4820 

i3 

46 

65i9 

66o5 

6691 

6777 

6863 

6949 

i3 

47 

4912 

5oo5 

5o98 

5i9i 

5283l5376 

12 

47 

7o35 

-7120 

-7206 

7292 

7378 

7464 

12 

48 

5469 
6024 

556i  5654 
61  17)62  10 

5747 
63o2 

5839|5932 
63956487 

II 

IO 

48 
49 

7549 
8o63 

7635 
8i49 

8235 

78o6 

8320 

7892 
84o6 

7978 
849i 

II 
10 

5o 

9.346579 

66-72  6764 

6857 

6949  7o4i 

9 

5o 

9.378577 

8662 

8748 

8833 

8919 

9oo4 

9 

5i 

7i34 

-7226  73i8 

74io 

75o37595 

8 

5i 

9o89 

9i75 

9260 

9346 

943i 

95i6 

8 

52 

7687 

77797871 

7963 

8o568i48 

7 

52 

96oi 

9687 

9772 

9857 

9942 

..28 

7 

53 

8240 

8332  8424 

85i6 

8608  87oo 

6 

53 

9.38oii3 

oi98 

0283 

o368 

o454 

o539 

6 

54 

8792 

8884189-76 

9o67 

9i59  925i 

5 

54 

0624 

o7o9 

0-794 

0879 

o964 

io49 

5 

55 

9343 

9435 

9526 

96i8 

97io  98o2 

4 

55 

1  1  34 

I2I9 

i3o4 

i389 

1474 

i559 

4 

56 

9893 

9985 

••77 

.168 

.260 

.352 

3 

56 

i643 

1-728 

i8i3 

i898 

i983 

2068 

3 

57 

9.35o443 

o535 

0626 

0-718 

o8o9 

0901 

2 

57 

2l52 

2237 

2322 

2406 

249I 

2576 

2 

58 

0992 

1084 

n75 

1266 

i358i449 

I 

58 

266l 

2745 

283o 

29i4 

2999 

3o84 

I 

59 

i54o 

i632  i723 

1814 

I9o6|i997 

O 

59 

3i68 

3253 

3337 

3422 

35o6 

359i 

0 

60" 

50"  !  40" 

30" 

20"   10" 

a 

60" 

50" 

40"   30" 

20"   10" 

d 

Co-sine  of  77  Degrees. 

1 

Co-sine  of  76  Degrees. 

1 

P  Part  5  l"  2"  3"  4"  5"  6//  7"  8//  9" 

p  p   (1"  2"  3"  4"  5"  6"  7"  8"  9" 

I  9  19  28  38  47  57  66  76  85 

{9  18  26  35  44  53  61  70  79 

LOGARITHMIC    TANGENTS. 


ri 

° 

Tangent  of  12  Degrees. 

I 

Tangent  of  13  Degrees. 

0" 

10" 

20" 

30" 

40" 

50" 

m 

0" 

10" 

20" 

30" 

40" 

50" 

o 

9.327475 

7578 

7682 

7785 

7888 

7992 

59 

o 

9.  363364 

346o 

3556 

3652 

3748 

3844 

59 

I 

8o95 

8i99 

8302 

84o5 

85o9 

8612 

58' 

i 

394o 

4o36 

4i32 

4228 

4324 

4420 

58 

2 

87i5 

8819 

8922 

9025 

9I28 

923l 

57 

2 

45i5 

46u 

4707 

48o3 

4899 

4994 

57 

3 

9334 

9438 

9541 

9644 

9747 

985o 

56 

3 

5o9o 

5i86 

5282 

5377 

5473 

5568 

56 

4 

9953 

..56 

.i59 

.262 

.365 

.468 

55 

4 

5664 

576o 

5855 

595i 

6o46 

6142 

55 

5 

9.330570 

o673 

0776 

o879 

0982 

1084 

54 

5 

6237 

6333 

6428 

6524 

66I9 

67i5 

54 

6 

1187 

1290 

i393 

i495 

i598 

1701 

53 

6 

6810 

69o5 

7001 

7096 

7i9i 

7287 

53 

7 

i8o3 

1906 

2008 

2III 

22l3 

23i6 

52 

7 

738a 

7477 

7572 

7668 

7763 

7858 

52 

8 

2418 

2521 

2623 

2726 

2828 

293o 

5i 

8 

7953 

8o48 

8i43 

8239 

8334 

8429 

5i 

9 

3o33 

3i35 

3237 

334o 

3442 

3544 

5o 

9 

8524 

8619 

8714 

88o9 

89o4 

8999 

5o 

10 

9.333646 

3  748 

385i 

3953 

4o55 

4i57 

49 

10 

9.369o94 

9i89 

9284 

9378 

9473 

9568 

49 

ii 

4259 

436i 

4463 

4565 

4667 

4769 

48 

ii 

9663 

9758 

9853 

9947 

..42 

.i37 

48 

12 

487i 

4973 

5o75 

5i77 

5279 

538o 

47 

12 

9.370232 

o326 

O42I 

o5i6 

0610 

o7o5 

47 

i3 

5482 

5584 

5686 

5788 

5889 

599i 

46 

i3 

°799 

o894 

o989 

io83 

n78 

I272 

46 

i4 

6093 

6194 

6296 

6398 

6499 

6601 

45 

i4 

i367 

i46i 

i556 

i65o 

1744 

i839 

45 

i5 

6702 

6804 

6905 

7oo7 

7io8 

7210 

44 

T5 

i933 

2028 

2122 

2216 

23ll 

24o5 

44 

16 

73n 

74i3 

?5i4 

76i5 

77I7 

7818 

43 

16 

2499 

2593 

2688 

2782 

2876 

297° 

43 

*7 

79  *  9 

8021 

8122 

8223 

8324 

8426 

42 

17 

3o64 

3i59 

3253 

3347 

344i 

3535 

42 

18 

8527 

8628 

8729 

883o 

893i 

9o32 

4i 

18 

3629 

3?23 

38i7 

39n 

4oo5 

4o99 

4i 

»9 

91  33 

9234 

933$ 

9436 

9537 

9638 

4o 

J9 

4i93 

4287 

438i 

4475 

4569 

4662 

4o 

20 

9.339739 

9840 

9941 

..42 

.i43 

.243 

39 

20 

9.374756 

485o 

4944 

5o38 

5i3i 

5225 

39 

21 

9.34o344 

o445 

o546 

o646 

0747 

o848 

38 

21 

53i9 

54i3 

55o6 

56oo 

5694 

5787 

38 

22 

b948 

1049 

n5o 

I25o 

i35i 

i45i 

37 

22 

588i 

5975 

6068 

6162 

6255 

6349 

37 

23 

i552 

i652 

1753 

i853 

i954 

2o54 

36 

23 

6442 

6536 

6629 

6723 

6816 

69io 

36 

24 

2i55 

2255 

2355 

2456 

2556 

2656 

35 

24 

7oo3 

7096 

7I9° 

7283 

7376 

747o 

35 

25 

2757 

2857 

2957 

3o57 

3i58 

3258 

34 

25 

7563 

7656 

775o 

7843 

7936 

8o29 

34 

26 

3358 

3458 

3558 

3658 

3758 

3858 

33 

26 

8122 

8216 

83o9 

8402 

8495 

8588 

33 

27 

3958 

4o58 

4i58 

4258 

4358 

4458 

32 

27 

8681 

8774 

8867 

896o 

9o53 

9i46 

32 

28 

4558 

4658 

4758 

4858 

4957 

5o57 

3i 

28 

9239 

9332 

9425 

95i8 

96n 

97o4 

3i 

29 

5i57 

5257 

5357 

5456 

5556 

5656 

3o 

29 

9797 

989o 

9983 

..75 

.168 

.261 

3o 

3o 

9.345755 

5855 

5954 

6o54 

6i54 

6253 

29 

3o 

9.38o354 

o446 

o539 

o632 

O725 

0817 

29 

3i 

6353 

6452 

6552 

665i 

6751 

685o 

28 

3i 

0910 

ioo3 

io95 

1188 

1280 

1373 

28 

32 

6949 

7049 

7i48 

7248 

?347 

7446 

27 

32 

i466 

i558 

i65i 

1743 

i836 

I928 

27 

33 

7545 

7645 

7744 

7843 

7942 

8042 

26 

33 

2020 

2Il3 

22O5 

2298 

239o 

2482 

26 

34 

8i4i 

8240 

8339 

8438 

8537 

8636 

25 

34 

2575 

2667 

2759 

2852 

2944 

3o36 

25 

35 

8735 

8834 

8933 

9o32 

9i3i 

923o 

24 

35 

3l29 

3221 

33i3 

34o5 

3497 

3589 

24 

36 

9329 

9428 

9527 

9626 

9724 

9823 

23 

36 

3682 

3774 

3866 

3958 

4o5o 

4i42 

23 

37 

9922 

.  .21 

.  I2O 

.218 

.817 

.4i6 

22 

37 

4234 

4326 

44i8 

45io 

4602 

4694 

22 

38 

9.35o5i4 

o6i3 

0712 

0810 

o9o9 

1007 

21 

38 

4786 

4878 

497o 

5o62 

5i53 

5245 

21 

39 

1106 

I2O4 

i3o3 

i4oi 

i5oo 

i598 

2O 

39 

5337 

5429 

552i 

56i2 

5704 

5796 

2O 

4o 

9.35i697 

I795 

i894 

I992 

2O9O 

2i89 

J9 

4o 

9  385888 

5979 

6o7i 

6i63 

6254 

6346 

J9 

4i 

2287 

2385 

2483 

2582 

2680 

2778 

18 

4i 

6438 

6529 

6621 

6712 

68o4 

6895 

18 

42 

2876 

2974 

3o73 

3i7i 

3269 

3367 

17 

42 

6987 

7o78 

7i7o 

7261 

7353 

7444 

i? 

43 

3465 

3563 

36Gi 

3759 

3857 

3955 

16 

43 

7536 

7627 

77i8 

7810 

79oi 

7992 

16 

44 

4o53 

4i5i 

4249 

4347 

4445 

4542 

i5 

44 

8o84 

8i75 

8266 

8358 

8449 

854o 

i5 

45 

464o 

4738 

4836 

4934 

5o3i 

5l29 

i4 

45 

863i 

8722 

88i4 

89o5 

8996 

9o87 

i4 

46 

5227 

5324 

5422 

5520 

56i7 

57i5 

i3 

46 

9178 

9269 

936o 

945i 

9542 

9633 

i3 

47 

58i3 

5910 

6008 

6io5 

6203 

63oo 

12 

47 

9724 

98i5 

99o6 

9997 

..88 

.179 

12 

48 

6398 

6495 

6593 

669o 

6787 

6885 

II 

48 

9.390270 

o36i 

o452 

o543 

o633 

0724 

II 

49 

6982 

7°79 

7177 

7274 

737i 

7469 

10 

49 

o8i5 

o9o6 

°997 

1087 

1178 

I269 

IO 

5o 

9.357566 

7663 

7760 

7857 

7954 

8o52 

9 

5o 

9.391360 

i45o 

i54i 

i632 

1722 

i8i3 

9 

5i 

8i49 

8246 

8343 

844o 

8537 

8634 

8 

5i 

1903 

i994 

2080 

2175 

2266 

2356 

8 

52 

873i 

8828 

8925 

9O22 

9119 

92l6 

7 

52 

2447 

2537 

2628 

2718 

2808 

2899 

7 

53 

93i3 

94o9 

95o6 

96o3 

9700 

9797 

6 

53 

2989 

3o8o 

3i7o 

3260 

335i 

344i 

6 

54 

9893 

999° 

..87 

.184 

.280 

.377 

5 

54 

353! 

3622 

37I2 

38o2 

3892 

3983 

5 

55 

9.36o474 

o57o 

0667 

o763 

0860 

o957 

4 

55 

4o73 

4i63 

4253 

4343 

4433 

4523 

4 

56 

io53 

n5o 

1246 

1  343 

i439 

i535 

3 

56 

46i4 

4704 

4794 

4884 

4974 

5o64 

3 

57 

i632 

I728 

1825 

I92I 

2017 

2Il4 

2 

57 

5i54 

5244 

5334 

5424 

55i4 

56o4 

2 

58 

22IO 

23o6 

24o3 

2499 

2595 

269I 

I 

58 

5694 

5783 

5873 

5963 

6o53 

6i43 

I 

59 

2787 

2884 

298o 

3o76 

3172 

3268 

0 

59 

6233 

6322 

64i2 

65o2 

6592 

6681 

0 

60" 

50"   40" 

30'' 

20" 

10" 

^ 

60"     50" 

40" 

30" 

20" 

10" 

• 

Co-tangent  of  77  Degrees. 

§ 

Co-tangent  of  76  Degrees. 

s 

p  p   C  1"  2"  3"  4"  5"  6"  7"  8"  9" 

.  C  1"  2"  3"  4"  5"  6"  7"  8"  9" 

I  10  20  30  40  50  60  70  80  90 

r.rari^  9  ig  2g  3?  46  f>6  65  74  gg 

LOGARITHMIC    SINES. 


.3 

Sine  of  14  Degrees. 

d 

Sine  of  15  Degrees. 

1 

0" 

10" 

20"   30"  j  40" 

50" 

9 

0" 

10" 

20" 

"30" 

40" 

50" 

0 

9.383675 

376o 

38443928i4oi3 

4o97 

59 

o 

9.4i2996 

3o75 

3i53 

3232 

33io 

3389 

59 

I 

4182 

4266 

435o443545i9 

46o3 

58 

I 

3467 

3546 

3624 

37o3 

378i 

386o 

58 

2 

4687 

4772 

4856494o5o24 

5io8 

57 

2 

3938 

4oi6 

4o95 

4i73 

4252 

433o 

57 

3 

4 

5l92 

5697 

5277 
578i 

536i  54455520. 
5865  5949'6o33 

56i3 
6n7 

56 
55 

3 

4 

44o8 
4878 

4486 
4956 

4565 
5o34 

4643 

5lI2 

472I 

5i9o 

48oo 
5269 

56 
55 

5 

6201 

6285 

63696452 

6536 

6620 

54 

5 

5347 

5425 

55o3 

558i 

5659 

5737 

54 

6 

6704 

6788 

6872  6955 

7o39 

7I23 

53 

6 

58i5 

5893 

597i 

6o49 

6l27 

6205 

53 

7 

7207 

729o 

7374  7458 

754i 

7625 

52 

7 

6283 

636i 

6439 

65i7 

6595 

6673 

52 

8 

7709 

7792 

7876  7959  8o43 

8l27 

5i 

8 

675i 

6828 

69o6 

6984 

7o62 

7i4o 

5i 

9 

8210 

820.4  83778461 

8544 

8627 

5o 

9 

7217 

7295 

7373 

745i 

7528 

76o6 

5o 

10 

9.  388711 

879488788961 

9o44 

9I28 

49 

10 

9.4i7684 

7761 

7839 

79i7 

7994 

8o72 

49 

ii 

92II 

92949378  946i 

9544 

9627 

48 

1  1 

8i5o 

8227 

83o5 

8382 

846o 

8537 

48 

12 

97" 

9794 

98779960 

..43 

.126 

47 

12 

86i5 

8692 

877o 

8847 

8925 

9002 

47 

i3 

9.3902IO 

o293  o376  o459 

o542 

0625 

46 

i3 

9°79 

9i57 

9234 

93l2 

9389 

9466 

46 

i4 

0708 

O79i  0874  o957 

io4o 

1123 

45 

i4 

9544 

962I 

9698 

9776 

9853 

993o 

45 

i5 

1206 

I289 

i37i 

1454 

i537 

1620 

44 

i5 

9.42OOO7 

oo85 

0162 

0239 

o3i6 

o393 

44 

16 

1703 

1786 

1868 

i95i 

2o34 

2117 

43 

16 

o47o 

o548 

0625 

0702 

°779 

o856 

43 

*7 

2i99 

22822365 

2447 

253o 

26i3 

42 

17 

o933 

IOIO 

io87 

n64 

1241 

i3i8 

42 

18 

2695 

2778 

2860 

2943 

3025 

3io8 

4i 

18 

i395 

1472 

i549 

1626 

I7o3 

1-780 

4i 

J9 

3i9i 

3273 

3356 

3438 

352o 

36o3 

4o 

!9 

i857 

I933 

2010 

2087 

ai64 

224l 

4o 

3O 

9.393685 

3768 

385o 

3932 

4oi5 

4o97 

39 

20 

9.4223l8 

2394 

247I 

2548 

2625 

27OI 

39 

21 

4179 

4262 

4344 

4426 

45o8 

459i 

38 

21 

2778 

2855 

293i 

3oo8 

3o85 

3i6i 

38 

22 

4673 

475548374919 

5O02 

5o84 

37 

22 

3238 

33i5 

339i 

3468 

3544 

362i 

37 

23 

5i66 

5348 

533o 

54i2 

5494 

5576 

36 

23 

3697 

3774 

385o 

3927 

4oo3 

4o8o 

36 

24 

5658 

5740  5822 

59o4 

5986 

6068 

35 

24 

4i56 

4233 

43o9 

4386 

4462 

4538 

35 

25 

6i5o 

6232  63i4 

6395 

6477 

6559 

34 

25 

46i5 

469i 

4767 

4844 

4920 

4996 

34 

26 

664i 

67236805 

6886 

6968. 

7o5o 

33 

26 

5o73 

5i49 

5225 

53oi 

5378 

5454 

33 

27 

7132 

7213  7295 

7377 

7458 

754o 

32 

27 

553o 

56o6 

5682 

5758 

5835 

59n 

32 

28 

7621 

77o3  7785 

•7866 

7948 

8o29 

3i 

28 

5987 

6o63 

6i39 

6ai5 

629i 

6367 

3i 

29 

8111 

8l92 

8274 

8355 

8437 

85i8 

3o 

29 

6443 

65i9 

6595 

6671 

6747 

6823 

3o 

3o 

9.3986oo 

8681 

8762 

8844 

8925 

9oo7 

29 

3o 

9.4268q9 

6975 

7o5i 

7127 

72O2 

7278 

29 

3i 

9o88 

9i69  925o 

9332 

94i3 

9494 

28 

3i 

7354 

743o 

75o6 

7582 

7657 

7733 

28 

32 

9575 

9657 

9738 

98i9 

99oo 

998i 

27 

32 

78o9 

7885 

796o 

8o36 

8112 

8i87 

27 

33 

9.  400062 

Ol44  0225 

o3o6 

o387 

o468 

26 

33 

'8263 

8339 

84i4 

8490 

8566 

864i 

26 

34 

o549 

06300711 

o792 

o873 

o954 

25 

34 

87i7 

8792 

8868 

8944 

9OI9 

9o95 

25 

35 

io35 

1116 

n97 

1277 

i358 

i439 

24 

35 

9i7o 

9246 

932I 

9397 

9472 

9547 

24 

36 

l520 

1601 

1682 

1762 

i843 

I924 

23 

36 

9623 

9698 

9774 

9849 

9924 

.... 

23 

-  37 

2005 

2085 

2166 

2247 

2328 

2408 

22 

37 

9.43oo75 

oi5o 

0226 

o3oi 

o376 

o45i 

22 

38 

2489 

257o  265o 

2731 

2811 

280,2 

21 

38 

o527 

0602 

o677 

0752 

0828 

o9o3 

21 

39 

297e 

3o53 

3i33 

32i4 

3294 

3375 

20 

39 

o978 

io53 

1128 

1203 

I278 

i354 

20 

4o 

9.4o3455 

3536  36i6 

3697 

3777 

3857 

I9 

4o 

9.43i429 

i5o4 

i579 

1  654 

I729 

1804 

'9 

4i 

3938 

4oi8 

4o98 

4i79 

4259 

4339 

18 

4i 

i879 

i954 

2O29 

2104 

2I79 

2254 

18 

4s 

4420 

45oo458o 

466o 

474i 

4821 

17 

42 

2329 

24o3 

2478 

2553 

2628 

27o3 

17 

43 

49oi 

4981 

5o6i 

5i4i 

5221 

5302 

16 

43 

2778 

2853 

2927 

3002 

3o77 

3i52 

16 

44 

5382 

5462 

5542 

5622 

5702 

5782 

i5 

44 

3226 

33oi 

3376 

345  1 

3525 

36oo 

i5 

45 

.5862 

5942 

6022 

6102 

6181 

6-261 

i4 

45 

3675 

3749 

3824 

3898 

3973 

4o48 

i4 

46 

634i 

6421 

65oi 

658  1 

6661 

674o 

i3 

46 

4122- 

419-7 

427I 

4346 

4420 

4495 

i3 

4? 

48 

6820 
7299 

69oo  698o 

7378  7458 

7o6o 
7538 

7i39 
76i7 

7219 
7697 

12 
II 

47 
48 

4569 
5oi6 

4644 
5o9i 

47i8 
5i65 

4793 
5239 

4867 
53x4 

4942 
5388 

12 
II 

'  49 

7777 

7856 

79368oi5 

8o95 

8i74 

10 

49 

5462 

5537 

56n 

5685 

576o 

5834 

10 

5o 

9.  4o8254 

8333 

84i3 

8492 

8572865i 

9 

5o 

9.4359o8 

5982 

6o56 

6i3i 

62o5 

6279 

9 

5i 

8731 

8810  8889 

8969 

9o48  9i27 

8 

5i 

6353 

6427 

65o2 

6576 

665o 

6724 

8 

52 

0,207 

0.286  9365 

9445 

952496o3 

7 

52 

6798 

6872 

6946 

7020 

7o94 

•7168 

1- 

53 

0,682 

9762.9841 

9920 

9999 

..78 

6 

53 

•7242 

73i6 

739o 

7464 

7538 

•7612 

6 

54 

9.4ioi57 

O237  o3i6 

o395 

o474 

o553 

5 

54 

7686 

776o 

7834 

79o8 

79Sl 

8o55 

5 

55 

o632 

0711 

o79o 

o869 

O948JIO27 

4 

55 

8i29 

82o3 

8277 

835i 

8424 

8498 

4 

56 

1  1  06 

n85 

1264 

i343 

1422 

i5oo 

3 

56 

8572 

8646 

87i9 

8793 

8867 

894i 

3 

57 

i579 

i658 

i737 

1816 

i895 

i973 

2 

57 

9oi4 

9o88 

9l62 

9235 

93o9 

9382 

2 

58 

2052 

2l3l 

2210 

2288 

2367 

2446 

I 

58 

9456 

953o 

96o3 

9677 

975o 

9824 

I 

59 

2524 

26o3 

2682 

276o 

2839 

29l8 

O 

59 

9897 

997i 

..44 

.118 

.101 

.265 

0 

GO" 

50" 

40" 

30" 

20" 

10" 

e 

60" 

50" 

40" 

30" 

20" 

10" 

c 

Co-sine  of  75  Degrees. 

i 

Co-sine  of  74  Degrees. 

5 

(I//   o"   Q' 

P  Pni-t)         J 

'  4"  5"  Q"  7"  8"  9" 

,  (  1"  2"  3"  4"  5"  6"  7"  8"  9" 

Ul}  8  16  24  33  41  49  57  65  73 

irt}  8  15  23  30  38  46  53  61  68 

LOGARITHMIC    TANGENTS. 


a 

Tangent  of  14  Degrees. 

a 

Tangent  of  15  Degrees. 

. 

0" 

10" 

20" 

30" 

40" 

50" 

m 

0" 

10" 

20" 

30" 

40" 

50" 

o 

9,396771 

6861 

695o 

7040 

7i3o 

72I9 

59 

o 

9.  428052 

8137 

8221 

83o5 

8389 

8473 

69 

i 

73o9 

7399 

7488 

7578 

7667 

7757 

58 

i 

8558 

8642 

8726 

8810 

8894 

8978 

58 

2 

7846 

7936 

8025 

8n5 

8204 

8294 

57 

2 

9062 

9i46 

923o 

93i4 

9398 

9482 

57 

3 

8383 

8472 

8562 

865i 

874o 

883o 

56 

3 

9566 

965o 

9734 

98i8 

9902 

9986 

56 

4 

8919 

9008 

9o98 

9l87 

9276 

9365 

55 

4 

9.430070 

oi54 

0237 

0321 

o4o5 

o489 

55 

5 

9455 

9544 

9633 

9722 

9811 

9900 

54 

5 

o573 

0657 

o74o 

0824 

0908 

0992 

54 

6 

999° 

••79 

.168 

.257 

.346 

.435 

53 

6 

1075 

iiSg 

1243 

i326 

i4io 

i494 

53 

7 

9  ,4oo524 

o6i3 

O7O2 

o79i 

0880 

0969 

52 

7 

i577 

1661 

1745 

1828 

1912 

i995 

52 

8 

io58 

ii4? 

1236 

i325 

i4i3 

1502 

5i 

8 

2079 

2162 

2246 

2329 

24l3 

2496 

5i 

9 

1591 

1680 

i769 

i857 

1946 

2035 

5o 

9 

258o 

2663 

2747 

283o 

2914 

2997 

5o 

10 

9.402124 

2212 

2301 

2390 

24-78 

2567 

49 

IO 

9.433o8o 

3i64 

3247 

333i 

34i4 

3497 

49 

ii 

2656 

2744 

2833 

2922 

3oio 

3o99 

48 

ii 

358o 

3664 

3747 

383o 

3914 

3997 

48 

12 

3187 

3276 

3364 

3453 

354i 

363o 

47 

12 

4o8o 

4i63 

4246 

433o 

44i3 

4496 

47 

i3 

37i8 

38o7 

3895 

3983 

4072 

4i6o 

46 

i3 

4579 

4662 

4745 

4828 

4912 

4995 

46 

i4 

4249 

4337 

4425 

45i4 

4602 

4690 

45 

U 

5o78 

5i6i 

5244 

5327 

54io 

5493 

45 

i5 

4778 

4867 

4955 

5o43 

5i3i 

5219 

44 

i5 

5^76 

5659 

5742 

5825 

5907 

599o 

44 

16 

53o8 

5396 

5484 

5572 

566o 

5748 

43 

16 

6o73 

6i56 

6239 

6322 

64o5 

6488 

43 

17 

5836 

5924 

6012 

6100 

6!88 

6276 

42 

17 

657o 

6653 

6736 

68i9 

6901 

6984 

42 

18 

6364 

6452 

654o 

6628 

67i6 

68o4 

4i 

18 

7o67 

7i5o 

7232 

73!5 

7398 

748o 

4i 

19 

6892 

6980 

7o68 

7i55 

7243 

733i 

4o 

J9 

7563 

7646 

7728 

7811 

7894 

7976 

4o 

20 

9.407419 

75°7 

7594 

7682 

777° 

7858 

39 

20 

9.438059 

8i4i 

8224 

83o6 

8389 

847i 

39 

21 

7945 

8o33 

8121 

8208 

8296 

8384 

38 

21 

8554 

8636 

8719 

8801 

8884 

8966 

38 

22 

8471 

8559 

8646 

8734 

8821 

8909 

37 

22 

9048 

9i3i 

92l3 

9296 

9378 

946o 

37 

23 

8996 

9084 

9171 

9259 

9346 

9434 

36 

23 

9543 

9625 

97°7 

979° 

9872 

9954 

36 

24 

9521 

9609 

9696 

9783 

9871 

9958 

35 

24 

9.44oo36 

0119 

0201 

0283 

o365 

o447 

35 

25 

9  .4ioo45 

oi33 

O22O 

o3o7 

o395 

0482 

34 

25 

o52g 

0612 

o694 

o776 

o858 

0940 

34 

26 

0569 

o656 

0743 

o83i 

0918 

ioo5 

33 

26 

IO22 

no4 

1186 

1268 

i35o 

i432 

33 

27 

1092 

1179 

1266 

i353 

i44i 

i528 

32 

27 

i5i4 

i596 

i678 

i76o 

1842 

1924 

32 

28 

i6i5 

1702 

1789 

i876 

i963 

2o5o 

3i 

28 

2006 

2088 

2I70 

2252 

2334 

2416 

3i 

29 

2  1  37 

2224 

23lO 

2397 

2484 

257I 

3o 

29 

249-7 

2579 

266l 

2743 

2825 

2907 

3o 

3o 

Q,  4i2658 

2745 

2832 

29I9 

3oo5 

3092 

29 

3o 

9.442988 

3070 

3i52 

3234 

33i5 

3397 

29 

3i 

3i79 

3266 

3352 

3439 

3526 

36i3 

28 

3i 

34-79 

356o 

3642 

3724 

38o5 

3887 

28 

32 

3699 

3786 

3873 

3959 

4o46 

4i32 

27 

32 

3968 

4o5o 

4l32 

4213 

4295 

4376 

27 

33 

4219 

43o6 

4392 

4479 

4565 

4652 

26 

33 

4458 

4539 

4621 

4702 

4784 

4865 

26 

34 

4?38 

4825 

4911 

4998 

5o84 

5i7i 

25 

34 

4947 

5o28 

5no 

5i9i 

5272 

5354 

25 

35 

5257 

5343 

543o 

55!6 

56o3 

5689 

24 

35 

5435 

55i7 

5598 

5679 

5761 

5842 

24 

36 

5775 

5862 

5948 

6o34 

6120 

620-7 

23 

36 

5923 

6oo5 

6086 

6167 

6248 

633o 

23 

37 

6293 

6379 

6465 

655i 

6638 

6724 

22 

37 

64n 

6492 

6573 

6654 

6735 

681-7 

22 

38 

6810 

6896 

6982 

7o68 

7i54 

7240 

21 

38 

6898 

6979 

-7060 

7141 

7222 

73o3 

21 

39 

7326 

74i3 

7499 

7585 

767i 

7757 

2O 

39 

7384 

7465 

7546 

7627 

7708 

7789 

20 

4o 

9.417842 

7928 

8014 

8100 

8186 

A 

8272 

J9 

4o 

9.44787° 

795i 

8o32 

8n3 

8i94 

8275 

19 

4i 

8358 

8444 

853o 

8616 

87oi 

8787 

18 

4i 

8356 

8437 

85i8 

8599 

8680 

8-760 

18 

42 

8873 

8959 

9044 

9i3o 

9216 

9302 

ll 

42 

884i 

8922 

9oo3 

9o84 

9i64 

9245 

J7 

43 

9387 

9473 

9559 

9644 

973o 

9816 

16 

43 

9326 

94o7 

9487 

9<<S 

9649 

973o 

16 

44 

99oi 

9987 

..72 

.1.58 

.244 

.329 

i5 

44 

9810 

989i 

9972 

.  .^2 

.i33 

.213 

i5 

45 

9.42o4i5 

o5oo 

o586 

o67i 

o757 

0842 

i4 

45 

9.450294 

o375 

o455 

o536 

0616 

o697 

i4 

46 

°927 

ioi3 

1098 

1184 

1269 

i354 

i3 

46 

0777 

o858 

o938 

ioi9 

io99 

1180 

i3 

47 

i44o 

i525 

1610 

i696 

i78i 

1866 

12 

47 

1260 

i34i 

1421 

i5o2 

i582 

1662 

12 

48 

I952 

2037 

2122 

22O7 

2292 

2378 

II 

48 

1743 

1823 

I9o3 

i984 

2084 

2i44 

II 

49 

2463 

2548 

2633 

27l8 

28o3 

2888 

IO 

49 

2225 

23o5 

2385 

2465 

2546 

2626 

IO 

5o 

9.422974 

3o59 

3i44 

3229 

33i4 

3399 

9 

5o 

9.452706 

2-786 

286-7 

20.47 

3027 

3io7 

9 

5i 

3484 

3569 

3654 

3739 

3824 

39o9 

8 

5i 

3i87 

3267 

3347 

3428 

35o8 

3588 

8 

52 

3993 

4o78 

4i63 

4248 

4333 

44i8 

7 

52 

3668 

3748 

3828 

39o8 

3988 

4o68 

7 

53 

45o3 

4587 

4672 

4757 

4842 

492-7 

6 

53 

4i48 

4228 

43o8 

4388 

4468 

4548 

6 

54 

Son 

5o96 

5i8i 

5265 

535o 

5435 

5 

54 

4628 

47o8 

4787 

4867 

4947 

5027 

5 

55 

55i9 

56o4 

5689 

5773 

5858 

5942 

4 

55 

6107 

5i87 

5267 

5346 

5426 

55o6 

4 

56 

602-7 

6112 

6196 

6281 

6365 

645o 

3 

56 

5586 

5655 

5745 

5825 

59o5 

5984 

3 

57 

6534 

66i9 

670^ 

6788 

6872 

6g56 

2 

5? 

6064 

6i44 

6223 

63o3 

6383 

6462 

2 

58 

7o4i 

7I25 

7210 

7294 

7378 

7463 

I 

58 

6542 

6622 

6-701 

6781 

6860 

694o 

I 

59 

7547 

763i 

77i5 

78oo 

7884 

7968 

O 

59 

7019 

7°99 

7178 

7258 

7337 

74i7 

O 

60" 

50" 

40" 

30"   20" 

10" 

a 

60"    |  50"   40"   30" 

20"   10"  |  d 

Co-tangent  of  75  Degrees. 

i 

Co-tangent  of  74  Degrees.   |  § 

„  T,  *  $  1"  2"  3"  4"  5"  6"  7"  8"  9" 

.C  1"  2"  3"  4"  5"  6"  7"  8"  9" 

r*  ravf1  / 

"}  9  17  26  35  43  52  61  69  78 

r.  rartj  g  J6  25  33  41  49  5?  65  74 

40 


LOGARITHMIC    SINES. 


A 

Sine  of  16  Degrees. 

d 

Sine  of  17  Decrees. 

s 

0" 

10" 

20" 

30" 

40" 

50" 

"S 

0" 

10"   20"   30"  1  40" 

50" 

0 

9.44o338 

o4n 

o485 

o558 

o632 

o7o5 

59 

O 

9.465935  6oo4  6o-3  6i4s  621  1 

6280 

59 

I 

0778 

o852 

0925 

0998 

1072 

n45 

58 

I 

6348 

64i7  6486  6555  6623 

6692 

58 

2 

1218 

1292 

i365 

i438 

i5u 

1  584 

57 

2 

676i 

683o6898 

6967 

7o36 

7io4 

57 

3 

i658 

i73i 

1804 

1877 

igSo 

2023 

56 

3 

7i73 

7242 

73io 

7379 

7448 

75i6 

56 

4 

2096 

2170 

2243 

23i6 

2389 

2462 

55 

4 

7585 

7653 

7722 

779° 

7859 

7928 

55 

5 

2535 

2608 

2681 

2754 

2827 

2900 

54 

5 

7996 

8o65 

8i33 

8202 

8270 

8338 

54 

6 

2973 

3o46 

3119 

3192 

3265 

3337 

53 

6 

8407 

8475 

85448612 

8681 

8749 

53 

7 

34io 

3483 

3556 

3629 

3702 

3774 

52 

7 

8817 

8886 

895419022 

9091 

9l59 

52 

8 

3847 

3920 

3993 

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9227 

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4284 

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2289 

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2628 

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17 

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783i 

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2966 

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3ioi 

3169 

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18 

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4i 

18 

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3575 

3642 

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3o 

9.  4-78142 

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29 

3i 

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28 

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32 

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9209 

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33 

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4761 

4832 

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33 

9342 

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9608 

9675 

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5327 

53q8 

25 

34 

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74 

25 

to  to  < 
0>  Ui4 

5469 
5893 

5539 
5963 

56io568i 
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575i 
6i75 

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24 
23 

35 
36 

7  I*** 

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24 
23 

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7936 

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2261 

2327 

2393 

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8357 

18 

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2525 

2591 

2657 

2723 

2789 

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42 

8427 

8497 

8567 

8638 

8708 

8778 

17 

42 

2921 

2987 

3o53 

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3i85 

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43 

8848 

8918 

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16 

43 

33i6 

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3646 

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44 

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9688 

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9828:9898  9968 

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48 

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48 

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56i7 

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49 

1  364 

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1712 

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49 

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1861 

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9.486o75 

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6206 

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6337 

6402 

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Si 

2199 

2268 

2338 

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8 

5i 

6467 

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6664 

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52 

2616 

2685 

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2963 

7 

52 

6860 

6925 

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7 

53 

3o32 

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3i7i 

324o33io 

3379 

6 

53 

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73i6 

7382 

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7577 

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54 

3448 

35i8 

3587 

3656 

3725 

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5 

54 

7643 

7708 

7773 

7838 

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7968 

5 

55 

3864 

3933 

4002 

4072 

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4210 

4 

55 

8o34 

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4 

56 

4279 

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4625 

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56 

8424 

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8684 

8749 

3 

57 

4694 

4763 

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49oi 

49-70 

5o39 

2 

57 

88i4 

8879 

8944 

9009 

9o74 

9i39 

2 

58 

5io8 

5i77 

5  a  46 

53i5 

5384 

5453 

I 

58 

92o4 

9269 

9334 

9399 

9464 

9528 

I 

59 

5522 

559i 

566o 

5729  5798 

5866 

O 

59 

9593 

9658 

9723 

9788 

9853 

9918 

O 

60" 

50" 

40" 

30"   20'' 

10" 

c  , 

60" 

50" 

40" 

30" 

20" 

10" 

J 

Co-sine  of  73 

Degrees. 

S 

Co-sine  of  72  Degrees. 

1 

5  1"  2"  3"  4" 

5"  6"  7"  8"  9" 

p  p  ,51"  2"  3"  4"  5"  6"  7"  8"  9" 

'  art}  7  14  21  28 

36  43  50  57  64 

'{  7  13  20  27  33  40  47  53  60 

LOGARITHMIC    TANGENTS. 


41 


1 

Tangent  of  1  6  Degrees. 

d 

Tangent  of  17  Degrees. 

s 

0"     10" 

20" 

30" 

40" 

50" 

* 

0" 

10" 

20" 

30"  |  40" 

50"' 

H™  
0 

9.457496J7576 

7655 

7735 

78i4 

7894 

59 

0 

9.485339 

54i4 

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5565|564o 

57i5 

59 

i 

7973 

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8i32 

8211 

829o 

837o 

58 

I 

579i 

5866 

594i 

6016 

6092 

6i67 

58 

2 

8449 

8528 

8608 

8687 

8766 

8846 

57 

2 

6242 

63i7 

6392 

6467 

6543 

6618 

57 

C 

8925 

900^ 

9o83 

9i63 

9242 

9321 

56 

G 

6693 

6768 

6843 

69i8 

6993 

7o68 

56 

4 

94oo 

9479 

9558 

9638 

9717 

9796 

55 

4 

7i43 

72l8 

7293 

7368 

7443 

75i8 

55 

r 

9875 

9954 

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.  I  12 

.270 

54 

c 

7593 

-7668 

7743 

78i8 

7893 

7968 

54 

6 

9.460349 

0428 

o5o7 

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o665 

o744 

53 

6 

8o43 

8118 

8i93 

8268 

8343 

84i8 

53 

7 

0823 

0902 

o98i 

1060 

n39 

1218 

52 

7 

8492 

8567 

8642 

8717 

8792 

8866 

52 

8 

I297 

i376 

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i533 

1612 

1691 

5i 

8 

894i 

9oi6 

9o9i 

9i66 

9240 

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9 

I77o 

1849 

1927 

2006 

2o85 

2  1  64 

5o 

9 

939o 

9465 

9539 

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9689 

9763 

5o 

10 

9.462242 

2321 

2400 

2478 

2557 

2636 

/ 

10 

9.489838 

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49 

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12 

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1  1  06 

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45 

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2370 

2445 

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16 

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5382 

546o 

43 

16 

25l9 

2593 

2668 

2742 

2816 

2890 

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5539 

56i7 

5695 

5773 

585i 

593o 

42 

17 

2965 

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3ll3 

3i87 

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3336 

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18 

6008 

6086 

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18 

34io 

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20 

9.466945 

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7179 

7257 

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20 

9.494299 

4373 

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4595 

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39 

21 

74i3 

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7569 

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7724 

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38 

21 

4743 

48i7 

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5o39 

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38 

22 

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37 

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23 

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858i 

8658 

8736 

36 

23 

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8969 

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24 

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35 

25 

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9668 

34 

25 

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6736 

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34 

26 

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27 

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27 

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28 

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io63 

3i 

28 

784i 

79i4 

7988 

8061 

8i35 

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3i 

29 

n4i 

1218 

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i373 

i45o 

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3o 

29 

8282 

8355 

8429 

85o2 

8575 

8649 

3o 

3o 

9.471605 

1682 

i759 

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1914 

1991 

29 

3o 

9.498722 

8796 

8869 

8943 

9oi6 

9089 

29 

3i 

2069 

2i46 

2223 

2300 

2377 

2455 

28 

3i 

9i63 

9236 

93o9 

9383 

9456 

9529 

28 

32 

2532 

2609 

2686 

2763 

2840 

2918 

27 

32 

96o3 

9676 

9749 

9822 

9896 

9969 

27 

33 

2995 

3072 

3i49 

3226 

33o3 

338o 

26 

33 

9.5ooo42 

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oi89 

0262 

o335 

0408 

26 

34 

3457 

3534 

36n 

3688 

3765 

3842 

25 

34 

o48i 

o555 

0628 

O7OI 

o774 

o847 

25 

35 

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3996 

4o73 

4i5o 

4227 

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24 

35 

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24 

36 

438i 

4458 

4535 

46I2 

4688 

4765 

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36 

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1432 

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1661 

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23 

37 

4842 

49i9 

4996 

5o73 

5i49 

5226 

22 

37 

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1870 

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2016 

2089 

2162 

22 

38 

53o3 

538o 

5456 

5533 

56io 

5687 

21 

38 

2235 

23o8 

238i 

2453 

2526 

2599 

21 

39 

5763 

584o 

59i7 

5993 

6o7o 

6i47 

20 

39 

26-72 

2745 

2818 

289I 

2964 

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9.476223 

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653o 

6606 

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4o 

9.5o3io9 

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3328 

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3473 

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6989 

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18 

4i 

3546 

36i9 

369i 

3764 

3837 

3910 

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42 

7142 

72i9 

7295 

7372 

7448 

7524 

17 

42 

3982 

4o55 

4128 

4200 

4273 

4346 

17 

43 

7601 

7677 

7754 

783o 

7go6 

7983 

16 

43 

44i8 

449i 

4563 

4636 

47Q9 

478i 

16 

44 

8059 

8i36 

8212 

8288 

8365 

844  1 

i5 

44 

4854 

4926 

4999 

5o72 

5i44 

52I7 

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45 

85i7 

8593 

867o 

8746 

8822 

8899 

i4 

45 

6289 

5362 

5434 

55o7 

5579 

5652 

i4 

46 

8975 

9o5i 

9I27 

92o3 

9280 

9356 

i3 

46 

5724 

5796 

5869 

594i 

6oi4 

6086 

i3  . 

47 

9432 

95o8 

9584 

966o 

9737 

98i3 

12 

47 

6i59 

623i 

63o3 

6376 

6448 

652O 

12 

48 

9889 

9965 

.  .41 

.117 

.i93 

.269 

II 

48 

6593 

6665 

6737 

6810 

6882 

6954 

II 

49 

9.48o345 

0421 

o497 

o573 

0649 

o725 

IO 

49 

7027 

7099 

7171 

7243 

73i6 

7388 

IO 

5o 

9.480801 

0877 

o953 

I029 

no5 

1181 

9 

5o 

9.5o746o 

7532 

76o5 

7677 

7749 

-7821 

9 

5i 

1257 

i333 

i4o8 

1  484 

i56o 

i636 

8 

5i 

7893 

7965 

8o38 

8110 

8182 

8254 

8 

52 

1712 

1788 

i863 

i939 

20l5 

209I 

7 

52 

8326 

8398 

847o 

8542 

86i4 

8687 

7 

53 

2167 

2242 

23i8 

2394 

2470 

2545 

6 

53 

8759 

883i 

89o3 

8975 

9047 

9119 

6 

54 

2621 

2697 

2772 

2848 

2924 

2999 

5 

54 

9191 

9263 

9335 

9407 

9479 

955i 

5 

55 

3o75 

3i5i 

3226 

33o2 

3377 

3453 

4 

55 

9622 

9694 

9766 

9838 

9910 

9982 

4 

56 

3529 

36o4 

368o 

3755 

383i 

39o6 

3 

56 

;.5ioo54 

0126 

oi98 

0269 

o34i 

o4i3 

3 

57 

3982 

4o57 

4i33 

4208 

4284 

4359 

2 

57 

o485 

o557 

o629 

o7oo 

o772 

o844 

2 

58 

4435 

45io 

4585 

466i 

4736 

4812 

I 

58 

o9i6 

o987 

io59 

n3i 

1203 

I274 

I 

59 

4887 

4962 

5o38 

5n3 

5i88 

5264 

O 

59 

1  346 

i4i8 

i489 

i56i 

i633 

i7o4 

O 

60" 

50"   40" 

30" 

20" 

10" 

a' 

tO" 

50" 

40" 

30" 

20" 

10" 

. 

Co-tangent  of  73  Degrees. 

ii 

Co  -tangent  of  72  Degrees. 

§ 

.(  \"  2"  3"  4"  5"  6"  7"  8"  9" 

P.  Part  J  g  15  23  31  39  46  54  62  7Q 

irl}  7   15  22  29  37  44  51  59  66 

LOGARITHMIC    SINES. 


.9 

Sine  of  18  Degrees. 

.5 

Sine  of  19  Degrees. 

i 

0" 

10" 

20" 

30"   40" 

50" 

a 

0" 

10" 

20" 

30" 

40" 

50" 

o 

9.489982 

..47 

.  112 

.177  .24l 

.3o6 

69 

o 

9.612642 

2703 

2764 

2825 

2886 

2948 

59 

I 

9.490371 

o436 

o5ooo565  o63o 

o695 

58 

I 

3009 

3070 

3i3i 

3192 

3253 

33i4 

58 

2 

o759 

0824 

o889o953  1018 

1082 

57 

2 

3375 

3436 

3497 

3558 

36i9 

368o 

57 

3 

1212 

12-76  i34i 

i4o5 

1470 

56 

3 

374i 

38o2 

3863 

3924 

3985 

4o46 

56 

4 

i535 

i599 

i664 

I728  i793 

1867 

55 

4 

4io7 

4i68 

4229 

4289 

435o 

44n 

55 

5 

1922 

i986 

2061 

2Il5  2I79 

2244 

54 

5 

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6 

53 

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1731 

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54 

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0680 

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54 

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2022 

2080 

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55 

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55 

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4 

56 

1172 

1233 

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3 

56 

-  266l 

2719 

2777 

2835 

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2961 

3 

57 

i54o 

1601 

1662 

1724 

1786 

1  846 

2 

57 

3O09 

3o67 

3i25 

3i83 

324i 

3299 

2 

58 

I9o7 

i969 

2030 

2091 

2162 

22l4 

I 

58 

3357 

34i5 

3473 

353i 

3589 

3647 

I 

69 

2276 

2336 

2397 

2458 

2620 

258l 

O 

69 

3704 

3762 

3820 

3878 

3936 

3994 

O 

60" 

50" 

40" 

30" 

20" 

10" 

. 

60" 

50" 

40" 

30" 

20" 

10" 

Co-sine  of  71  Degrees. 

a 

Co-sine  of  70  Degrees. 

.5 

Si 

f  -til  nil  q/ 

P  Part)    " 

'  4» 

5''  6"  7"  8"  9" 

P  P»rt5  !"   2"   3"   4"   5"   6"   7"  8"  9" 

ml  6  13  19  25 

31  38  44  50  57 

irt}  6  12  18  24  30  36  42  48  54 

LOGARITHM    j    TANGENTS. 


43 


A 

Tangent  of  18  Degrees. 

a 

Tangent  of  19  Degrees. 

- 

8 

ov 

10" 

20" 

30" 

40" 

50" 

3 

0" 

10" 

20" 

30" 

40" 

50" 

o 

9.5n776 

1  848 

1919 

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2o63 

2i34 

5g 

o 

9.5369-72 

7040 

7io9 

7177 

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59 

i 

2206 

2277 

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2492 

2564 

58 

I 

7382 

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75i9 

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2 

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2921 

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57 

2 

7792 

7860 

7929 

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3 

3o64 

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3421 

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3 

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4 

3493 

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55 

4 

8611 

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8747 

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5 

3921 

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4206 

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54 

5 

9020 

9088 

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9,224 

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4 

6 

4349 

4420 

4492 

4563 

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53 

6 

9429 

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3 

7 

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7 

9837 

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2 

8 

5275 

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9.540245 

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9 

563i 

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10 

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1943 

2010 

2078 

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16 

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16 

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3635 

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3837 

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18 

9458 

9529 

9600 

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18 

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4377 

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19 

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20 

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39 

20 

9.545119 

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5254 

5322 

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39 

21 

0728 

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0869 

o939 

IOIO 

1080 

38 

21 

5524 

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5726 

5793 

586o 

38 

22 

n5i 

1221 

1292 

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i432 

i5o3 

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22 

5928 

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23 

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1  643 

1714 

1784 

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23 

633i 

6398 

6466 

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6600 

6667 

36 

24 

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2206 

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24 

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6802 

6869 

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35. 

25 

2417 

2487 

2557 

2627 

2698 

2-768 

34 

25 

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34 

26 

2838 

2908 

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3119 

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33 

26 

754o 

7608 

7675 

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33 

27 

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27 

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8211 

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28 

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28 

8345 

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29 

4ioo 

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4240 

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438o 

445o 

3o 

29 

8747 

88i4 

8881 

8948 

9oi5 

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9.52452O 

459o 

466o 

473o 

48oo 

487o 

29 

3o 

9.549i49 

9216 

9283 

9349 

94i6 

9483 

29 

3i 

4g4o 

5009 

5o79 

5i49 

52I9 

5289 

28 

3i 

955o 

9617 

9684 

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98i7 

9884 

28 

32 

5359 

5429 

5499 

5568 

5638 

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27 

32 

995i 

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..85 

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27 

33 

5778 

5848 

59i8 

5987 

6057 

612-7 

26 

33 

9.55o352 

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26 

34 

6i97 

6266 

6336 

64o6 

6476 

6545 

25 

34 

0752 

0819 

0886 

0952 

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1086 

25 

35 

66i5 

6685 

6754 

6824 

6894 

6963 

24 

35 

n53 

1219 

1286 

i353 

1419 

i486 

24 

36 

7o33 

7io3 

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7242 

73l2 

738i 

23 

36 

i552 

1619 

1686 

1752 

1819 

i885 

23 

37 

745  1 

7520 

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7660 

7729 

7799 

22 

37 

I952 

20I9 

2o85 

2l52 

2218 

2285 

22 

38 

7868 

7938 

8oo7 

8077 

8i46 

8216 

21 

38 

235i 

24l8 

2484 

255i 

26l7 

2684 

21 

39 

8285 

8355 

8424 

8494 

8563 

8633 

20 

39 

2750 

2817 

2883 

2950 

3oi6 

3o8-3 

2O 

4o 

9.528-702 

8772 

884i 

8910 

898o 

9049 

19 

4o 

9.553i49 

32i6 

3282 

3348 

34i5 

348  1 

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4i 

9119 

9188 

9257 

9327 

9396 

9465 

18 

4i 

3548 

36i4 

368o 

3747 

38i3 

388o 

18 

42 

9535 

96o4 

9673 

9743 

98l2 

9881 

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42 

3946 

4012 

4o79 

4i45 

4211 

4278 

17 

43 

995i 

.  .20 

..89 

.158 

.228 

•297 

16 

43 

4344 

44io 

4476 

4543 

4609 

4675 

16 

44 

9.53o366 

o435 

o5o4 

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44 

4741 

48o8 

4874 

4g4o 

5oo6 

5o73 

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45 

P78i 

o85o 

O920 

0989 

io58 

1127 

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45 

5i39 

52o5 

527I 

5337 

54o4 

547o 

i4 

46 

1196 

1265 

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i473 

I  542 

i3 

46 

5536 

56o2 

5668 

5734 

58oo 

5867 

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4? 

161  1 

1680 

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1818 

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12 

47 

5933 

5999 

6o65 

6i3i 

6i97 

6263 

12 

48 

2025 

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2i63 

2232 

2301 

2370 

II 

48 

6329 

6395 

646  1 

6527 

6593 

6659 

II 

49 

2439 

25o8 

2577 

2646 

27l5 

2784 

10 

49 

6725 

679i 

6857 

692^ 

6989 

7o55 

10 

5o 

9.532853 

292I 

2990 

3o59 

3i28 

3i97 

9 

5o 

9.557121 

7187 

7253 

73i9 

7385 

745i 

9 

5i 

3266 

3335 

34o4 

3472 

354i 

36io 

8 

5i 

75i7 

7583 

7649 

778i 

7847 

8 

52 

3679 

3748 

38i6 

3885 

3954 

4023 

7 

52 

7913 

7978 

8o44 

8110 

8176 

8242 

7 

53 

4092 

4i6o 

4229 

4298 

4367 

4435 

6 

53 

83o8 

8373 

8439 

85o5 

857i 

8637 

6 

54 

45o4 

4573 

464i 

47io 

4779 

4847 

5 

54 

87o3 

8768 

8834 

8900 

8966 

9o3] 

5 

55 

4916 

4985 

5o53 

5l22 

5i9i 

5259 

4 

55 

9°97 

Ql62 

9229 

929^ 

936o 

9426 

4 

56 

5328 

5396 

5465 

5534 

5602 

5671 

3 

56 

949i 

9557 

9623 

9688 

9754 

9820 

3 

57 

5739 

58o8 

5876 

5945 

6oi3 

6082 

2 

$7 

9885 

995i 

.  .17 

..82 

.i48 

.214 

2 

58 

6i5o 

6219 

6287 

6356 

6424 

6493 

I 

58 

9.56o279 

o345 

o4io 

o476 

o542 

o6o7 

I 

59 

656i 

663o 

6698 

6767 

6835 

6903 

O 

59 

067^ 

o738 

o8o4 

o869 

o935 

IOOO 

O 

60"    |  50"   40" 

30" 

20" 

10" 

a 

60" 

50" 

40" 

30" 

20" 

10" 

d 

Co-tangent  of  7  1  Degrees. 

•9 

s 

Co-tangent  of  70  Degrees. 

1 

p  Part$  1"  2"  3"  4"  5"  6"  7"  8"  9" 
I  7  14  21  28  35  42  49  56  63 

P.  Part  J  7  13  2Q  -7  33  4Q  47  54  6Q 

44 


LOGARITHMIC    SINES. 


c 

Sine  of  20  Degrees. 

.3 

Sine  of  21  Degrees. 

S 

0" 

10" 

20" 

30" 

40" 

50" 

™ 

0" 

10" 

20" 

30" 

40" 

50" 

0 

9.534o52 

4i  10 

4i67 

4225 

4283 

434i 

59 

0 

9.554329 

4384 

4439 

4494 

4549 

46o3 

59 

i 

4399 

4456 

45i4 

4572 

463o 

4687 

58 

i 

4658 

47i3 

4768 

4822 

4877 

4932 

58 

2 

4745 

48o3 

486i 

49i8 

4976 

5o34 

57 

2 

4987 

5o42 

5o96 

5i5i 

52o6 

5260 

57 

3 

5o92 

5i4g 

5207 

5265 

5322 

538o 

56 

3 

53i5 

537o 

5425 

5479 

5534 

5589 

56 

4 

5438 

5495 

555356io 

5668 

5726 

55 

4 

5643 

5698 

5753 

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34 
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49 

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53    2018 

2074 

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53 

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2349 

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2625 

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54 

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56 

2323 

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2427 

2479  2532 

2584 

3 

57 

334i 

3396 

345  1 

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2 

57 

2636 

2688 

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2793i2845 

289? 

2 

58 

367o 

3725 

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3835;389o 

3945 

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58 

295o 

3002 

3o54 

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3210 

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59 

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4o55 

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4i65  4219 

4a74 

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59 

3263  33i5 

3367 

34i9347i 

3523 

O 

60"     50" 

40" 

30"   20"   10" 

fl 

60"     50" 

40" 

30"   20" 

10" 

c- 

Co-sine  of  69  Degrees. 

i 

Co-sine  of  68  Degrees. 

.5 
S 

<  1"  2"  3"  4" 

5"  6"  7"  8"  9" 

.(  I"  2"  3"  4"  5"  6"  7"  8"  9" 

art{  6  11  17  23 

28  34  39  45  51 

i 

r.rart^  5  n  lg  21  ^  ^  ^  ^  4g 

LOGARITHMIC    TANGENTS. 


1 

Tangent  of  20  Degrees. 

A 

Tangent  of  21  Degrees. 

8 

0" 

10" 

20" 

30" 

40" 

50" 

2 

0" 

10" 

20" 

30" 

40" 

50" 

o 

9.56io66 

n3i 

1197 

1262 

1328 

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59 

0 

9-  584i77 

4240 

43o3 

4366 

4429 

4492 

59 

I 

i459 

i524 

i59o 

i655 

1721 

1786 

58 

I 

4555 

46i8 

468  1 

4?44 

48o6 

4869 

58 

2 

i85i 

1917 

I982 

2048 

2Il3 

2178 

57 

2 

4932 

4995 

5o58 

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5i83 

5246 

57 

3 

2244 

23o9 

2375 

244o 

25o5 

2571 

56 

3 

53o9 

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5435 

5498 

556o 

5623 

56 

4 

2636 

2701 

2767 

2832 

2897 

2963 

55 

4 

5686 

5749 

58ii 

5874 

5937 

6000 

55 

5 

3028 

3o93 

3i58 

3224 

3289 

3354 

54 

5 

6062 

6125 

6188 

625i 

63i3 

6376 

54 

6 

34i9 

3485 

355o 

36i5 

368o 

3746 

53 

6 

6439 

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6564 

6627 

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53 

7 

38n 

3876 

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52 

7 

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7128 

52 

8 

4202 

4267 

4332 

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4462 

4527 

5i 

8 

7i9o 

7253 

73i6 

7378 

744i 

75o3 

5i 

9 

4593 

4658 

4723 

4788 

4853 

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9 

7566 

7629 

7691 

7754 

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10 

9.564983 

5o48 

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49 

IO 

9.58794i 

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ii 

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48 

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83  1  6 

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12 

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9003 

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46 

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35 

24 

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35 

25 

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34 

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26 

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27 

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1  645 

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28 

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29 

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5027 

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9.572738 

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2994 

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9.595398 

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5583 

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32 

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3636 

3700 

3764 

3828 

27 

32 

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6200 

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6446 

27 

33 

3892 

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4020 

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26 

33 

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6693 

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6816 

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34 

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18 

4i 

9459 

9520 

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9643 

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4s 

734i 

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7659 

17 

42 

9827 

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9949 

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7723 

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0929 

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1174 

1235 

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8867 

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8994 

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1601 

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9248 

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5375 

9438 

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47 

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1  846 

1907 

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12 

48 

9629 

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9819 

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9946 

II 

48 

2029 

2090 

2l5l 

2212 

2273 

2334 

II 

49 

9.58ooo9 

0072 

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0199 

0262 

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IO 

49 

2395 

2456 

2517 

2578 

2639 

2700 

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5o 

9.58o389 

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0642 

0706 

9 

5o 

9.602761 

2822 

2883 

2944 

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3o66 

9 

5i 

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o896 

0939 

1022 

1086 

8 

5i 

3127 

3i88 

3249 

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337i 

3432 

8 

52 

n4o 

1212 

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i339 

I4O2 

i465 

7 

52 

3493 

3554 

36i5 

3675 

3736 

3797 

7 

53 

i528 

i59i 

i655 

1718 

1781 

1  844 

6 

53 

3858 

39!9 

398o 

4o4i 

4lO2 

4162 

6 

54 

I907 

1971 

2034 

2097 

2l6o 

2223 

5 

54 

4223 

4284 

4345 

44o6 

4467 

4527 

5 

55 

2286 

235o 

24i3 

2476 

2539 

2602 

4 

55 

4588 

4649 

4?io 

4771 

483i 

4892 

4 

56 

2665 

2728 

279i 

2854 

29I7 

298o 

3 

56 

4953 

5oi4 

5o74 

5i35 

5i96 

5257 

3 

*7 

3o44 

3107 

3i7o 

3233 

3296 

3359 

2 

57 

53i7 

5378 

5439 

55oo 

556o 

562i 

2 

58 

3422 

3485 

3548 

36n 

3674 

3737 

I 

58 

5682 

5742 

58o3 

5864 

5924 

5985 

I 

59 

38oo 

3863 

3926 

3989 

4o52 

4n4 

0 

59 

6o46 

6106 

6167 

6228 

6288 

6349 

O 

60" 

50" 

40" 

30" 

20" 

10" 

a 

60" 

50"  |  40" 

30" 

20" 

10" 

. 
a 

Co-tangent  of  69  Degrees. 

S 

Co-tangent  of  68  Degrees. 

i 

p  p.  (  1"  2"  3"  4"  5"  6"  7"  8"  9" 

p  p   <  1"  2"  3"  4"  5"  6"  7"  8"  9" 

$  6  13  19  26  32  39  45  51  58 

irlj  6  12  19  25  31  37  43  49  56 

46 


LOGARITHMIC    SINES. 


.a 

Sine  of  22  Degrees. 

d 

Sine  of  23  Degrees. 

B 

0" 

10" 

20"   30"   40" 

50" 

jjj 

0" 

10" 

20" 

30" 

40" 

50" 

o 

9.573575 

3628 

368o37323784 

3836  59 

0 

9.59i878 

I928 

I977 

2027 

20-76 

2126 

59 

I 

3888 

394o 

3992  4o44  4o96 

4i4858 

I 

2176 

2225 

2275 

2324 

2374 

2423 

58 

2 

4200 

4262 

43o44356,44o8 

446o 

57 

2 

2473 

2522 

2572 

2621 

26-71 

2720 

57 

3 

45ia 

4564 

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4772 

56 

3 

2770 

28l9 

2869 

29i8 

2968 

3017 

56 

4 

4824 

4876 

4928  498o  5o32 

5o84 

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4 

3067 

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3264 

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55 

5 

5i36 

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5 

3363 

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6 

5447 

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6 

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7 

5758 

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7 

3955 

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16 

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16 

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18 

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21 

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9.58oo85 

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9,582840 

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29 

3o 

9.6oo7oo 

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29 

3i 

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3297 

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32 

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32 

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27 

33 

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33 

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26 

34 
35 
36 

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486749x8 

25 
24 
23 

34 
35 
36 

1860 
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24 
23 

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22 

37 

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28-72 

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38 

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21 

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45 

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7838 

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12 

47 

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5749 

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12 

48 
49 

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II 
IO 

48 
49 

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594o 
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II 
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9 

5o 

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6655 

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5i 

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8 

5i 

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6798 

6846 

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6989 

8 

52 

9489 

9539  9589  9639 

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52 

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53 

9789 

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9988;..38 

6 

53 

7322 

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7464 

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6 

54 

9.690088 

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0237 

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5 

54 

76o7 

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7702 

7749 

7797 

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5 

55 

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4 

55 

7892 

7939 

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8082 

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4 

56 

0686 

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3 

56 

8177 

8224 

827I 

83i9 

8366 

84i4 

3 

57 

0984 

io34 

io84 

n33 

H83J233 

2 

57 

846  1 

85o8 

8556 

86o3 

865i 

8698 

a 

58 

1282 

i332 

i382 

i43i 

i48i  i53i 

I 

58 

8745 

8793 

884o 

8887 

8935 

8982 

i 

5g 

1680 

i63o  1680 

1729 

i779  1828 

O 

59 

9029 

9°77 

9I24 

9171 

92I9 

9266 

0 

60" 

50" 

40" 

30"   20"   10" 

. 

60" 

50" 

40" 

30" 

20" 

10" 

c 

Co-sine  of  67  Degrees. 

a 

Co-sine  of  66  Degrees.     a" 

PPartJ1"  2"  3/ 

'  4"  5"  6"  7"  8"  9" 

p  p   (  1"  2"  3"  4"  5"  6"  7"  8"  9" 

\  5  10  15  20  25  31  36  41  46 

ff  I  5  10  15  19  24  29  34  39  44 

LOGARITHMIC    TANGENTS. 


4-7 


1 

Tangent  of  22  Degrees. 

J 

Tangent  of  23  Degrees. 

s 

0" 

10" 

20"  |  30"   40"   50" 

2 

0" 

10" 

20" 

30"  1  40" 

50" 

o 

9.606410 

6470 

653l 

6691 

6652 

6713 

59 

o 

9.627852 

•7910 

7969 

8028 

8086 

8:45 

59 

i 

6773 

6834 

6894 

69  5  5 

7oi5 

7076 

58 

i 

8203 

8262 

8320 

8379 

8437 

8496 

58 

2 

3 

4 

7i37 
7600 
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7923 

7258  73i8 
7621  76811 
7984  8o44i 

7379 

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7439 
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8i65 

^7 
56 
55 

2 

3 
4 

8554 
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8963 
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8671 
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8788 
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8846 
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57 
56 
55 

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8225 

8286 

8346 

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54 

5 

9606 

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6 

8588 

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8890 

53 

6 

9956 

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53 

1 

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7 

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52 

8 

9312 

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8 

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5i 

9 

9674 

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ioo5 

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1122 

1180 

1238 

1296 

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10 

9.6ioo36 

0096 

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49 

TO 

9.63i355 

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16 

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16 

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2621 

2681 

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17 

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18 

2921 

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18 

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9.6i364i 

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20 

9.  634838 

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5069 

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21 

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38 

21 

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22 

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22 

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37 

23 

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36 

23 

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24 

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35 

24 

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35 

25 

5435 

5495 

5555 

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34 

25 

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34 

26 

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33 

26 

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7207 

33 

27 

6i5i 

6211 

627I 

633o 

639o 

645o 

32 

27 

7265 

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7438 

7495 

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32 

28 

6509 

6569 

6628 

6688 

6748 

6807 

3i 

28 

76n 

7668 

7726 

7783 

7841 

7899 

3i 

29 

6867 

6926 

6986 

7o46 

7io5 

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3o 

29 

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8oi4 

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8187 

8244 

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9  617224 

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29 

3i 

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28 

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8647 

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32 

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27 

32 

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9280 

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33 

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8533 

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26 

33 

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9452 

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26 

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883o 

889o 

8949 

25 

34 

9682 

9740 

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99I2 

9969 

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35 

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24 

35 

9.64oo27 

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36 

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37 

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22 

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22 

38 

9.620076 

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21 

38 

1060 

1117 

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1232 

1289 

1  346 

21 

39 

0432 

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19-76 

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18 

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2091 

2148 

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42 

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42 

2434 

2491 

2549 

2606 

2663 

2720 

17 

43 

i852 

1911 

i97o 

2029 

2088 

2147 

16 

43 

2777 

2834 

2892 

2949 

3oo6 

3o63 

16 

44 

2207 

2266 

2325 

2384 

2443 

25O2 

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44 

3l20 

3i77 

3235 

3292 

3349 

34o6 

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45 

256i 

2620 

26-79 

2738 

2797 

2856 

i4 

45 

3463 

3520 

3577 

3634 

3691 

3749 

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46 

2915 

2974 

3o33 

3092 

3i5i 

32IO 

i3 

46 

38o6 

3863 

3920 

3977 

4o34 

4o9i 

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47 

3269 

3328 

3387 

3446 

35o5 

3564 

12 

47 

4i48 

42o5 

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43  1  9 

4376 

4433 

12 

48 

3623 

3682 

374i 

38oo 

3858 

39i7 

II 

48 

4490 

4547 

46o4 

466i 

4718 

4775 

II 

49 

3976 

4o35 

4o94 

4i53 

4212 

4271 

IO 

49 

4832 

4889 

4946 

5oo2 

5o6o 

5n7 

IO 

5o 

9.62433o 

4388 

4447 

45o6 

4565 

4624 

Q 

5o 

9.645i74 

523i 

5288 

5345 

54o2 

5459 

9 

5i 

4683 

4742 

48oo 

4859 

4918 

4977 

& 

5i 

55i6 

5573 

563o 

5687 

5744'58oi 

8 

62 

5o36 

5og4 

5i53 

5212 

5271 

533o 

7 

52 

5857 

5gi4 

597' 

6028 

6o856i42 

7 

53 

5388 

5447 

55o6 

5565 

5623 

5682 

6 

53 

6199 

6256 

63i3 

6369 

64266483 

6 

54 

574i 

58oo 

5858 

59I7 

5976 

6o35 

5 

54 

654o 

6597 

6654 

6710 

6767;6824 

5 

55 

6o93 

6i52 

6211 

6269 

6328 

6387 

4 

55 

6881 

6938 

6995 

7o5i 

7io8;7i65 

4 

56 

6445 

65o4 

6563 

6621 

6680 

6739 

3 

56 

7222 

7279 

7335 

7392 

7449  75°6 

3 

57 

6797 

6856 

69i5 

6973 

7032 

7090 

2 

57 

7562 

7619 

7676 

7733 

7789*7846 

2 

58 

7149 

7208 

•7266 

7325 

7383 

7442 

I 

58 

79o3 

7960  8016:807!: 

8i3o8i86 

I 

59 

75oi 

7559 

76i8 

7676 

7735 

7793 

0 

59 

8243 

83oo835684i3 

8470:8626 

0 

60" 

50" 

40" 

30" 

20" 

10" 

. 

60"    |  50"  |  40"  |  30" 

20"  1  10" 

. 

Co-tangent  of  67  Degrees. 

S3 

Co-tangent  of  66  Degrees. 

a 

P  P  A  I"  2"  3"  4"  5"  6"  7"  8"  9" 

.(  1"  2"  3"  4"  5"  6"  7"  8"  9" 

trc£  6  12,  18  24  30  36  42  48  54 

in\  6  12  17  23  29  35  40  46  52 

LOGARITHMIC    SINES. 


FT 

Sine  of  24  Degrees. 

a 

Sine  of  25  Degrees. 

• 

0" 

10" 

20" 

|  30" 

40" 

50" 

9 

0"     10"   20"   30" 

40V 

50" 

0 

I 

9  6o93i3 
9597 

936i 
9644 

9691 

9455 
9739 

9502 
9786 

955o 
9833 

59 
58 

o 

I 

9.625948 
6219 

5993 
62^4 

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9.633984 

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28 

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33 

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8788 
9064 

26 

25 

33 

34 

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49io 
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52i8 

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26 
25 

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9i56 

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9294 

9340 

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35 

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5394 

5438 

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24 

36 

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9432 

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9616 

23 

36 

557o 

56i4 

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23 

37 

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22 

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21 

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9.  6.  02  i  3 

0259 

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20 

39 

636o 

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42 

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1084 

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1  17511221 

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42 

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7192 

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7323 

7367 

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43 

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16 

43 

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1861 
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45 
46 

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8066 

8328 

8110 
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8i53 

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47 

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2454 

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2637 

12 

47 

8458 

85o2 

8546 

8589 

8633 

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12 

48 

3682 

2728 

2773 

28i9 

2865 

2910 

II 

48 

8720 

8763 

8807 

885i 

8894 

8938 

II 

49    2956 

3ooi 

3o47 

3o92 

3i38 

3i83 

10 

49 

8981 

9025 

9068 

9I  12 

9i55 

9*99 

10 

5o  9.623229 

3274 

3320 

3365 

34n 

3456 

9 

5o 

9.639242 

9286 

9329 

9373 

94i6 

946o 

9 

5i 

35o2 

3547 

3593  3638 

3683 

3729 

8 

5i 

95o3 

9546 

959o 

9633 

9677 

9720 

8 

52 

3774 

3820 

3865 

39n 

3956 

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7 

52 

9764 

9807 

985i 

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9937 

998i 

7 

53    4o47 

4092 

4i38 

4i83 

4228 

4274 

6 

53 

9.640024 

0068 

on  i 

oi98 

024l 

6 

54 

43i9 

4364 

44io 

445545oo 

4546 

5 

54 

0284 

o328 

0371 

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o5oi 

5 

55 
56 

459i 
4863 

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4682 
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4999  5o44 

48i8 
5o89 

4 
3 

55 
56 

o544  o588 
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o63i 
o89i 

o674o7i8 
0934:0978 

o76i 

1  02  I 

j 

5? 

5i35 

5i8o 

5225 

5270  53i6 

536i 

2 

57 

1064  1  107 

i  i5i 

1  194  i237 

1280 

2 

58 

54o6 

545i 

5496 

5542  5587 

5632 

I 

58 

i324  i367 

i4io 

i453  !496 

i54o 

I 

59 

5677 

5722 

5768 

58i3;5858 

59o3 

O 

59 

i583  1626 

1669 

1712  i756  1799  o 

60" 

50" 

40"  J 

30"   20" 

10" 

B 

60"     50"   40"   30"   20"  i  10"  1  ^ 

Co-sine  of  65 

Degrees. 

Co-sine  of  64  Degrees.     ^ 

P  T>  tf  1"  2"  3"  4" 

5"  6"  7"  8"  9" 

p  p   (  1"  2"  3"  4"  5"  6"  7"  S"  9"  1 

P'Part{  5   9  14  18 

23  28  32  37  42 

ij 

^4   9  13  18  22  26  31  35  40 

LOGARITHMIC    TANGENTS. 


49 


A 

Tangent  of  24  Degrees. 

A 

Tangent  of  25  Degrees. 

m 

0" 

10" 

20" 

30" 

40" 

50" 

m 

0" 

10" 

20" 

30" 

40" 

50" 

o 

9.648583 

864o 

8696 

8753 

88lO 

8866 

59 

o 

9.  668673 

8728 

8782 

8837 

8892 

8947 

59 

1 

8923 

898o 

9o36 

9o93 

9i5o 

92O6 

58 

I 

9OO2 

9°57 

9112 

9167 

9222 

9277 

58 

2 

9263 

93i9 

9376 

9433 

9489 

9546 

57 

2 

9332 

9387 

9442 

9497 

9552 

9606 

57 

3 

9602 

9659 

97i5 

9772 

9829 

9885 

56 

3 

966i 

9716 

9771 

9826 

988l 

9936 

56 

4 

9942 

9998 

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.in 

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55 

4 

999  1 

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55 

5 

9.650281 

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o394 

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54 

5 

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54 

6 

0620 

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53 

6 

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0923 

53 

7 

0959 

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1128 

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1241 

52 

7 

0977 

1032 

087 

1142 

1197 

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52 

8 

1297 

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l4lO 

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1579 

5i 

8 

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4i6 

1470 

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i58o 

5! 

9 

i636 

1692 

i749 

i8o5 

1861 

1918 

5o 

9 

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1689 

744 

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1908 

5o 

10 

9.65i974 

2031 

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2i43 

220O 

2256 

49 

10 

9.671963 

2018 

2072 

2127 

2182 

2236 

49 

ii 

a3ifl 

2369 

2425 

2481 

2538 

2594 

48 

ii 

229*1 

2346 

2400 

2455 

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2564 

48 

12 

^65o 

2707 

2763 

2819 

2875 

2932 

47 

12 

2619 

2674 

2728 

2783 

2838 

2892 

47 

1  3 

J988 

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3ioi 

3i57 

32i3 

3269 

46 

i3 

2947 

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3m 

3i65 

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46 

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3382 

3438 

3494 

355i 

3607 

45 

i4 

3274 

3329 

3384 

3438 

3493 

3547 

45 

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3663 

37i9 

3776 

3832 

3888 

3944 

44 

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3657 

37n 

3766 

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44 

16 

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4169 

4225 

4281 

43 

16 

3929 

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4202 

43 

J7 

4337 

4394 

445o 

45o6 

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42 

J7 

43n 

4366 

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4475 

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18 

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473i 

4787 

4843 

4899 

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4i 

18 

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4638 

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5i23 

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20 

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54o4 

546o 

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39 

20 

9.675237 

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21 

5684 

5740 

5796 

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5908 

5964 

38 

21 

5564 

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5727 

5781 

5836 

38 

22 

6020 

6076 

6i32 

6188 

6244 

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37 

22 

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5945 

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6108 

6162 

37 

23 

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36 

23 

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6271 

6325 

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36 

24 

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6748 

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6860 

6916 

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35 

24 

6543 

6597 

665i 

6706 

6760 

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35 

25 

7028 

7084 

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7196 

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34 

25 

6869 

6923 

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34 

26 

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33 

26 

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7466 

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27 

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32 

27 

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32 

28 

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28 

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8008 

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3i 

29 

8369 

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848  1 

853-7 

8592 

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3o 

29 

8171 

8225 

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8334 

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3o 

3o 

9.658704 

876o 

8816 

8871 

8927 

8983 

29 

3o 

9.678496 

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8604 

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29 

3i 

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9262 

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28 

3i 

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28 

32 

9373 

9429 

9485 

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27 

32 

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27 

33 

0.708 

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9819 

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26 

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26 

34 

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25 

34 

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9958 

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25 

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24 

36 

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23 

36 

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1266 

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22 

38 

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1  544 

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21 

38 

1092 

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1254 

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21 

39 

1710 

1766 

1821 

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20 

39 

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1470 

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20 

4o 

9.  662o43 

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18 

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2225 

2279 

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1  8 

42 

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2765 

2820 

2876 

2931 

2987 

17 

42 

2387 

2440 

2494 

2548 

2602 

2656 

17 

43 

3o42 

3o97 

3i53 

3208 

3264 

33i9 

16 

43 

2710 

2764 

28l7 

2871 

2925 

2979 

16 

44 

3375 

343o 

3485 

354l 

3596 

365i 

i5 

44 

3o33 

3o87 

3i4o 

3i94 

3248 

33o2 

i5 

45 

37o7 

3762 

38i8 

3873 

3928 

3984 

i4 

45 

3356 

34io 

3463 

35i7 

3571 

3625 

i4 

46 

4o39 

4o94 

4i5o 

42o5 

4260 

43i6 

i3 

46 

3679 

3732 

3786 

384o 

3894 

3947 

i3 

47 

4371 

4426 

4482 

4537 

4592 

4648 

12 

47 

4ooi 

4o55 

4109 

4162 

4216 

4270 

12 

48 

47o3 

4758 

48i4 

4869 

4924 

4979 

II 

48 

4324 

4377 

443  1 

4485 

4539 

4592 

II 

49 

5o35 

5o9o 

5i45 

5200 

5256 

53n 

10 

49 

4646 

4700 

4753 

4807 

486i 

49i4 

10 

5o 

9.  665366 

542i 

5477 

5532 

5587 

5642 

9 

5o 

9.684968 

5022 

5o75 

5  1  29 

5i83 

5236 

9 

5i 

5698 

5753 

58o8 

5863 

59i8 

5974 

8 

5i 

5290 

5344 

5397 

545i 

55o5 

5558 

8 

52 

6o29 

6o84 

6139 

619^ 

6240, 

63o5 

7 

52 

56i2 

5666 

57i9 

5773 

5827 

588o 

7 

53 

636o 

64i5 

6470 

6525 

658o 

6636 

6 

53 

5934 

5987 

6o4i 

6o95 

6i48 

6202 

6 

54 

669i 

6746 

6801 

6856 

69n 

6966 

5 

54 

6255 

63o9 

6363 

64i6 

6470 

6523 

5 

55 

7021 

7076 

7l32 

7187 

7242 

7297 

4 

55 

6577 

663o 

6684 

6737 

6791 

6845 

4 

56 

7352 

7407 

7462 

75i7 

7572 

7627 

3 

56 

6898 

6952 

7oo5 

7059 

7112 

•7166 

3 

57 

7682 

7737 

7792 

7847 

79°3 

7958 

2 

57 

72I9 

7273 

7326 

738o 

7433 

7487 

2 

58 

8oi3 

8068 

8i23 

8178 

8233 

8288 

I 

58 

y54o 

759^ 

7647 

7701 

7754 

78o8 

I 

59 

8343 

8398 

8453 

85o8 

8563 

8618 

O 

59 

7861 

79i5 

7968 

8021 

8075 

8128 

0 

60" 

50" 

40" 

30"  1  20" 

10" 

. 

60" 

50" 

40" 

30" 

20" 

10" 

j 

Co-tangent  of  65  Degrees. 

a 

Co-tangent  of  64  Degrees. 

s 

r  !//  2//  3//  4//  5//  6//  7//  8"  9" 

(  1"  2"  3"  4"  5"  6"  7"  8"  9" 

in{  6  11  17  22  28  33  39  45  50 

art{  5  11  16  22  27  33  38  43  49 

50 


LOGAIIIHMIC    SINES. 


.9 

Sine  of  26  D  -grees. 

d 

Sine  of  27  Degrees. 

I 

0" 

10"p  20"p  1  0"  '  40"  J  NV' 

3 

0" 

10'  H 

20" 

30"  |  40" 

50" 

o 

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58 

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58 

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59 

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1490 

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0 

60" 

40"  |  30" 

20"  j  10" 

a 

60" 

50" 

40" 

30" 

20"   10" 

a 

Co-sine  of  63  Degrees. 

i 

Co-sine  of  62  Degrees. 

1 

P  Part  5  !"  2//  3//  4//  5"  6"  7"  8'   9" 

p  p  .(!"  2"  3"  4"  5"  6"  7"  8"  9" 

I  4   8  13  17  21  25  30  34  38 

{T  I  4   8  12  16  20  24  28  32  36 

LJGARITHMIC    TANGENTS. 


.3 

Tangent  of  26  Degrees. 

0 

Tangent  of  27  Degrees. 

SI 

0" 

10" 

20" 

30" 

40"   50" 

S 

0" 

10" 

20" 

30" 

40"   50" 

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9.688182 

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42 

9.  720160, 

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2047 

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16 

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2257 

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2362 

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2466 

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26-76 

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1191 

1243 

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i4 

46 

278l 

2833 

2885 

2938 

2990 

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1600 

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3i47 

3i99 

3252 

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3356 

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47 

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1906 

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12 

48 

34o9 

346i 

35i3 

3566 

36i8 

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I  I 

48 

2009 

2060 

2III 

2162 

22l3 

2264 

II 

49 

3722 

3775 

3827 

3879 

3932 

3984 

IO 

49 

23  1  5 

2366 

24l7 

2468 

2519 

2570 

10 

5o 

9.7o4o36 

4o88 

4i4i 

4i93 

4245 

4297 

9 

5o 

9.  -722621 

26-72 

2723 

2774 

2825 

2876 

9 

5i 

435o 

4402 

4454 

45o6 

4559 

46n 

8 

5i 

2927 

2978 

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3o8o 

3i3o 

3i8i 

8 

52 

4663 

47i5 

4768 

4820 

4872 

4924 

7 

52 

3232 

3283 

3334 

3385 

3436 

3487 

7 

53 

4976 

5o29 

5o8i 

5i33 

5i85 

5237 

6 

53 

3538 

3589 

364o 

3691 

3742 

3793 

6 

54 

529o 

5342 

5394 

5446 

5498 

555i 

5 

54 

3844 

3895 

3945 

3996 

4o47 

4o98 

5 

55 

56o3 

5655 

5707 

5759 

58n 

5863 

4 

55 

4i49 

4200 

425i 

4302 

4353 

44o3 

4 

56 

59i6 

5968 

6020 

6o72 

6124 

6176 

3 

56 

4454 

45o5 

4556 

46o7 

4658 

47Q9 

3 

57 

6228 

6280 

6333 

6385 

6437 

6489 

2 

57 

476o 

48io 

486i 

49I2 

4963 

5oi4 

2 

58 

654i 

6593 

6645 

6697 

6749 

6801 

I 

58 

5o65 

5u5 

5i66 

52i7 

5268 

53i9 

I 

59 

6854 

69o6 

6958 

-7010 

-7062 

7114 

O 

59 

537o 

5420 

547i 

5522 

5573J5624 

O 

60" 

50" 

40" 

30" 

20" 

10" 

. 

60" 

50" 

40" 

30" 

20"   10" 

^ 

Co-tangent  of  63  Degrees. 

S 

Co-tangent  of  62  Degrees. 

s 

p  p  A  I"  2"  3"  4"  5"  6"  7"  8"  9" 

(  V  2"  3"  4"  5"  6"  7"  8"  9" 

I  5  11  16  21  26  32  37  42  47 

ar  >  5  10  15  21  26  31  36  41  46 

52 


LOGARITHMIC    SINES. 


d 

Sine  of  28  Degrees. 

g 

Sine  of  29  Degrees. 

s 

0" 

10" 

20" 

30" 

40" 

50" 

9 

0" 

10"   20"   30"  l  40" 

50" 

0 

9.671609 

1649 

1688 

I728 

i768 

i8o7 

59 

o 

9.68557i 

56o9  5647 

5685 

5723 

576i 

59 

I 

i847 

1886 

1926 

i965 

2005 

2o45 

58 

I 

5799 

5837 

5875 

59i3 

595i 

5989 

58 

2 

2084 

2124 

2i63 

2203 

2242 

2282 

57 

2 

6o27 

6o65 

6io36i4i 

6i78 

6216 

57 

3 

2321 

236i 

2400 

2440 

2479 

2519 

56 

3 

6254 

6292 

633o!6368 

64o6 

6444 

56 

4 

2558 

2598 

2637 

2677 

27l6 

2756 

55 

4 

6482 

6519 

6557 

6595 

6633 

667i 

55: 

5 

2795 

2835 

2874 

2914 

2953 

2992  54 

5 

67o9 

6747 

6785 

6822 

6860 

6898 

54; 

6 

3o32 

3071 

3m 

3i5o 

3190 

322953 

6 

6936 

6974 

7OI2 

7o49 

7o87 

7I25 

53 

7 

3268 

33o8 

334?  3387 

3426 

3465  52 

7 

7i63 

7201 

7238 

7276 

73i4 

7352 

52 

8 

35o5 

3544 

3583  3623 

3662  3702  5i 

8 

7389 

7427 

7465 

75o3 

754i 

7578 

5ii 

9 

374i 

3780 

38203859 

38983938 

5o 

9 

7616 

7654 

7692 

7729 

7767 

78o5 

5o 

10 

9.673977 

4oi6 

4o56  4095 

4i34'4i73 

49 

10 

9.  687843 

7880 

79i8 

7956 

7993 

8o3i 

49 

ii 

42l3 

4252 

4291 

433i 

437o'44o9 

48 

ii 

8o69 

8106 

8i44 

8182 

8220 

8257 

48 

12 

4448 

4488 

45274566 

46o64645 

47 

12 

8295 

8333 

837o 

84o8 

8446 

8483 

47 

i3 

4684 

4723 

4762:4802 

484i  488o 

46 

i3 

852i 

8559 

8596 

8634 

867i 

87o9 

46 

i4 

4919 

4959 

4998:5037 

5o76  5n5 

45 

i4 

8747 

8784 

8822 

8860 

8897 

8935 

45 

i5 

5i55 

5i94 

52335272 

53n 

535o 

44 

i5 

8972 

9010 

9o48 

9o85 

9I23 

9i6o 

44 

16 

5390 

5429 

5468  55o7 

5546  5585 

43 

16 

9i98 

9235 

9273 

93n 

9348 

9386 

43 

J7 

5624 

5664 

57o35742 

578i  5820 

42 

*7 

9423 

9461 

9498 

9536 

9573 

96n 

42 

18 

5859 

5898 

59375976 

6016  6o55 

4i 

18 

9648 

9686 

9723 

976i 

9798 

9836 

4i 

19 

20 

60946133 
9.6763286367 

6172  621  1 
64o66445 

625o  6289 
64846523 

4o 
39 

*9 

20 

9873 
9.600098 

9911 
oi36 

9948 
0173 

9986 

02  I  I 

..23 

0248 

..61 
0286 

4o 
39 

21 

656266oi 

664o  6679 

67i86757 

38 

21 

'o323 

o36i 

o398 

o435 

o473 

o5io 

38 

22 

67966835 

68746913 

6952  6991 

37 

22 

o548 

o585 

0622 

0660 

o697 

o735 

37 

23 

7o3o 

7069 

71087147 

7i86  7225 

36 

23 

0772 

0809 

0847 

o884 

0922 

o959 

36 

24 

7264 

73o3 

7342  7381 

•7420  -7459 

35 

24 

0996 

io34 

1071 

no8 

n46 

n83 

35 

25 

7498 

7536 

7575  76i4 

76537692 

34 

25 

1220 

1258 

I295 

i332 

i37o 

i4o7 

34 

26 

773i 

777° 

•78097848 

7886  7925 

33 

26 

1  444 

1482 

i5i9 

i556 

i594 

i63i 

33 

27 

7964 

8oo3 

80428081 

8i2o8i58 

32 

27 

1668 

1706 

1743 

i78o 

i8i7 

i855 

32 

28 

8197 

8236 

8275^83i4 

8353  839i 

3i 

28 

1892 

1929 

i966 

2004 

2041 

2078 

3i 

29 

843o 

8469 

85o88547 

85858624 

3o 

29 

2Il5 

2i53 

2I9O 

2227 

2264 

2302 

3o 

3o 
3i 

9.678663 
8895 

8702 
8934 

87408779 
8973  9012 

88i8|8857 
goSo  9089 

29 

28 

3o 
3i 

9.692339 
i562 

2376 
2599 

24i3 
2636 

245o 
2674 

2488 

27II 

2525 

2748 

29 

28 

32 

9128 

9167 

9205  9244 

9283 

932I 

27 

32 

2785 

2822 

2859 

2897 

2934 

297I 

27 

33    9360 

9399 

94389476 

95i5 

9554 

26 

03 

3oo8 

3o45 

3o82 

3119 

3i57 

3i94 

26 

34    9692 

963i 

9670  9708 

9747 

9786 

25 

34 

323i 

3268 

33o5 

3342 

3379 

34i6 

25 

35    9824 

9863 

99029940 

9979 

..17 

24 

35 

3453 

3490 

3528 

3565 

36o2  3639 

24 

369.68oo56 

0095 

oi33  0172  0210 

0249 

23 

36 

3676 

37i3 

375o 

3787 

3824 

386i 

23 

3? 

0288 

o326 

o365  o4o3  0442  o48i 

22 

37 

3898- 

3935 

3972 

4009 

4o46 

4o83 

22 

38 

o5ig 

o558 

o596orns  06730712 

21 

38 

4l2O 

4i57 

4194 

423i 

4268  43o5 

•I 

Sg1    o75o 

0789 

0828  0866  0905  0943 

2O 

39 

4342 

4379 

44i6 

4453 

449o4527 

2O 

409.680982 

IO2O 

io59  1097 

u36 

n74 

'9 

4o 

9.694564 

46oi 

4638 

4675 

47.  2  4749 

'9 

4i    I2i3 

I25l 

1290  i328  i366 

i4o5 

18 

4i 

4786 

4823 

486o 

4897 

4934497> 

i  a 

42    i443 

1482 

l520 

iSSg  i597 

i636 

17 

42 

5007 

5o44 

5o8i 

5n8 

5i55'5i92 

17 

431    1674 

I7i3 

1751 

1789 

1828 

1866 

16 

43 

5229 

5266 

53o3 

5339 

5376 

54i3 

16 

44    1905 

1943 

1981 

2O2O 

2o58 

2097 

i5 

44 

545o 

5487 

5.524 

556i 

5598 

5634 

i5 

45    2i35 

2173 

2212 

225o 

2288 

2327 

i4 

45 

567i 

57o8 

5745 

578258i9 

5855 

i4 

46    2365 

24o3 

2442 

2480  2519 

2557 

i3 

46 

5892 

5929 

5966 

6oo3  6039 

6o76 

i3 

47    2595 

2633 

2672 

2710  2748 

2787 

12 

47 

6n3 

6i5o 

6187 

6223  6260 

6297 

12 

48:   2825 

2863 

2902 

2940  2978 

3oi6 

II 

48 

6334 

6370 

6407 

6444i648i 

65i7 

II 

49    3o55 

3o93 

3i3i 

3170  3208 

3246 

IO 

49 

6554 

659i 

6628 

6664'67oi 

6738 

10 

509.683284 

3323 

336i 

3399  3437 

3475 

9 

5o 

9.696775 

6811 

6848 

6885 

692I 

6958 

9 

5i    35i4 

3552 

3590 

3628  3667 

37o5 

8 

5i 

6995 

7o3i 

7068 

7io5 

7i4i 

7178 

8 

52!    3y43 

378i 

38i9 

3858  3896 

3934 

7 

52 

72l5 

725i 

7288 

7325 

736i 

7398 

7 

53i    3972 

4oio 

4o48 

40874125 

4i63 

6 

53 

7435 

7471 

75o8 

7545 

758i 

76i8 

6 

54    4201 

4239 

4277 

43i54353 

4392 

5 

54 

7654 

769i 

7728 

7764 

78oi 

7838 

5 

55j    443o 

4468 

45o6 

45444582 

4620 

4 

55 

7874 

79n 

7947 

7984  8020 

8o57 

4 

56    4658 

4696 

4735 

477348ii 

4849 

3 

56 

8o94 

8i3o 

8167 

82038240 

8276 

3 

57    4887 

4925 

4963 

5ooi|5o39 

5o77 

2 

57 

83i3 

8349 

8386 

8423  8459 

8496 

2 

58 

5n5 

5i53 

5191 

5229^267 

53o5 

I 

58 

8532 

8569 

86o5 

8642  8678 

87i5 

I 

59 

5343 

538i 

54i9 

5457  5495 

5533 

0 

59 

875i 

8788 

8824 

886i|8897 

8934 

0 

60" 

50" 

40" 

30"   20" 

10" 

c 

60" 

50" 

40" 

30"   20" 

10" 

a 

Co-sine  of  6  1  Degrees. 

§ 

Co-sine  of  60  Degrees. 

i 

t<  \"  2"  3"  4"  5"  6"  7"  8"  9" 
in\  4  8  12  16  19  23  27  31  35 

p  p  .  <  1"  2"  3"  4"  5"  6"  7"  8"  9" 
irt}  4   7  11  15  19  22  26  30  33 

LOGARITHMIC    TANGENTS. 


53 


1 

Tangent  of  28  Degrees. 

c 

Tangent  of  29  Degrees. 

s 

0" 

10" 

20" 

30" 

40" 

50" 

9 

0" 

10" 

20" 

30" 

40" 

50" 

o 

9.725674 

5725 

5776 

5827 

5878 

5928 

59 

0 

9.743752 

3802 

385i 

39oi 

395i 

4ooo 

59 

I 

5979 

6o3o 

6081 

6i3i 

6182 

6233 

58 

I 

4o5o 

4o99 

4i49 

4i99 

4248 

4298 

58 

2 

6284 

6334 

6385 

6436 

6487 

6537 

57 

2 

4348 

4397 

4447 

4496 

4546 

4596 

57 

r 
C 

6588 

6639 

669o 

674o 

6791 

6842 

56 

/; 

4645 

4695 

4744 

4794 

4844 

4893 

56 

i. 

6892 

6943 

6994 

7o45 

7°95 

7i46 

55 

4 

4943 

4992 

5o42 

5o92 

5i4i 

5i9i 

55 

t 

7197 

7247 

7298 

7349 

7399 

745o 

54 

c 

524o 

529o 

5339 

5389 

5439 

5488 

54 

6 

75oi 

755i 

7602 

7653 

77°3 

7754 

53 

6 

5538 

5587 

5637 

5686 

5736 

5785 

53 

7 

76o5 

7855 

79o6 

7957 

8007 

8o58 

52 

7 

5835 

5884 

5934 

5983 

6o33 

6082 

52 

8 

8109 

8i59 

8210 

8261 

83n 

8362 

5i 

8 

6i32 

6182 

623i 

6281 

633o 

638o 

5i 

9 

8412 

8463 

85i4, 

8564 

86i5 

8665 

5o 

9 

6429 

6479 

6528 

6577 

6627 

6676 

5o 

10 

9.728716 

8767 

8817 

8868 

8918 

8969 

49 

IO 

9.746726 

6775 

6825 

68  74 

6924 

69'/3 

49 

ii 

9020 

9070 

9I2I 

9171 

9222 

9272 

48 

ii 

7023 

7072 

7122 

7171 

7221 

7270 

48 

12 

9323 

9374 

9424 

9475 

9525 

9576 

47 

12 

73i9 

7369 

74i8 

7468 

7517 

7567 

47 

i3 

9626 

9677 

9727 

9778 

9828 

9879 

46 

i3 

7616 

7665 

77i5 

7764 

7814 

7863 

46 

i4 

9929 

998o 

..3o 

..81 

.132 

.182 

45 

i4 

79i3 

7962 

8011 

8061 

8110 

8160 

45 

i5 

9.73o233 

0283 

o333 

o384 

0434 

o485 

44 

i5 

8209 

8258 

83o8 

8357 

84o6 

8456 

44 

16 

o535 

o586 

o636 

0687 

0737 

0788 

43 

16 

85o5 

8555 

86o4 

8653 

87o3 

8752 

43 

i? 

o838 

o889 

o939 

°99° 

io4o 

1091 

42 

!7 

8801 

885i 

89oo 

8949 

8999 

9o48 

42 

18 

n4i 

u9i 

1242 

I292 

1  343 

i393 

4i 

18 

9°97 

9i47 

9i96 

9245 

9295 

9344 

4i 

J9 

i444 

i494 

1  544 

i595 

1645 

i696 

4o 

T9 

9393 

9443 

9492 

954i 

959i 

964o 

4o 

20 

9.73i746 

i796 

1847 

i897 

i948 

i998 

39 

20 

9-749689 

9739 

9788 

9837 

9886 

9936 

39 

21 

2048 

2o99 

2l49 

2200 

2250 

23oo 

38 

21 

9985 

..34 

..84 

.133 

.182 

.23l 

38 

22 

235i 

2401 

245  1 

2502 

2552 

2602 

37 

22 

9.  750281 

o33o 

o379 

0428 

0478 

o527 

37 

23 

2653 

2703 

2753 

28o4 

2854 

29o4 

36 

23 

o576 

o625 

o675 

0724 

o773 

0822 

36 

24 

2955 

3oo5 

3o55 

3io6 

3i56 

32o6 

35 

24 

0872 

092I 

o97o 

ioi9 

1069 

1118 

35 

25 

3257 

33o7 

3357 

34o8 

3458 

35o8 

34 

25 

1167 

1216 

1265 

i3i5 

1  364 

i4i3 

34 

26 

3558 

36o9 

3659 

37°9 

376o 

38io 

33 

26 

1462 

i5n 

i56i 

1610 

i659 

1708 

33 

27 

386o 

39io 

396i 

4on 

4o6i 

4m 

32 

27 

i757 

1806 

i856 

I9o5 

1954 

2003 

32 

28 

4162 

4212 

i262 

43i2 

4363 

44i3 

3i 

28 

2O52 

2IOI 

2l5l 

220O 

2249 

2298 

3i 

29 

4463 

45i3 

4564 

46i4 

4664 

47i4 

3o 

29 

2347 

2396 

2446 

2495 

2544 

2593 

3o 

3o 

9.734764 

48i5 

4865 

49i5 

4965 

5oi5 

29 

3o 

9.  752642 

269I 

2740 

2789 

2839 

2888 

29 

3i 

5o66 

5i  16 

5i66 

52i6 

5266 

53i7 

28 

3i 

2937 

2986 

3o35 

3o84 

3i33 

3i82 

28 

32 

5367 

5417 

5467 

55i7 

5567 

56i8 

27 

32 

323i 

3280 

333o 

3379 

3428 

3477 

27 

33 

5668 

57i8 

5768 

58i8 

5868 

59i8 

26 

33 

3526 

3575 

3624 

3673 

3722 

377i 

26 

34 

5969 

6oi9 

6069 

6n9 

6i69 

62I9 

25 

34 

3820 

3869 

39i8 

3967 

4oi6 

4o66 

25 

35 

6269 

63i9 

6370 

6420 

6470 

6520 

24 

35 

4n5 

4:64 

4213 

4262 

43n 

436o 

24 

36 

6570 

6620 

6670 

6720 

6770 

6820 

23 

36 

44o9 

4458 

45o7 

4556 

46o5 

4654 

23 

3? 

6870 

6921 

6971 

7021 

7071 

7121 

22 

37 

4703 

4752 

48oi 

485o 

4899 

4948 

22 

38 

7171 

7221 

7271 

7321 

737i 

7421 

21 

38 

4997 

5o46 

5o95 

5i44 

5i93 

5242 

21 

39 

7471 

7521 

7571 

7621 

7671 

7721 

2O 

39 

529I 

534o 

5389 

5438 

5487 

5536 

2O 

4o 

9.787771 

7821 

7871 

792I 

7971 

8021 

J9 

4o 

9.  755585 

5634 

5682 

5731 

5780 

5829 

I9 

4i 

8071 

8121 

8171 

8221 

8271 

832i 

18 

4i 

5878 

5927 

5976 

6o25 

6074 

6i23 

18 

42 

8371 

8421 

8471 

852i 

857i 

8621 

I7 

42 

6l72 

6221 

62-70 

63i9 

6368 

64i6 

I7 

43 

8671 

8721 

8771 

8821 

887i 

892I 

16 

43 

6465 

65i4 

6563 

6612 

6661 

6710 

16 

44 

8971 

9O2I 

9°7I 

9I2I 

9,1?1 

922I 

i5 

44 

6759 

6808 

6857 

6905 

6954 

7oo3 

i5 

45 

9271 

932I 

937i 

9420 

947o 

952O 

i4 

45 

7o52 

7IOI 

7i5o 

7199 

7247 

7296 

i4 

46 

957° 

962O 

9670 

9720 

9770 

9820 

i3 

46 

7345 

7394 

7443 

7492 

?54i 

7589 

i3 

4? 

9870 

9920 

9969 

..I9 

..60 

.II9 

12 

47 

7638 

7687 

7736 

7785 

7834 

7882 

12 

48 

9.740169 

O2I9 

0269 

o3i9 

o368 

0418 

II 

48 

793! 

798o 

8o29 

8078 

8127 

8i75 

II 

49 

o468 

o5i8 

o568 

0618 

0668 

0717 

IO 

49 

8224 

8273 

8322 

837i 

84i9 

8468 

IO 

5o 

9.740767 

0817 

0867 

0917 

o967 

1016 

9 

5o 

9.7585i7 

8566 

86i5 

8663 

8712 

8761 

9 

5i 

1066 

1116 

166 

1216 

1265 

i3i5 

8 

5i 

8810 

8858 

89o7 

8956 

9oo5 

9o53 

8 

52 

i365 

i4i5 

465 

i5i4 

i564 

1614 

7 

52 

9I02 

9i5i 

9200 

9248 

9297 

9346 

7 

53 

i664 

i7i4 

763 

i8i3 

i863 

I9i3 

6 

53 

9395 

9443 

9492 

954i 

959o 

9638 

6 

54 

1962 

2OI2 

2062 

2112 

2161 

2211 

5 

54 

9687 

9736 

9785 

9833 

9882 

993i 

5 

55 

2261 

23ll 

36o 

24lO 

2460 

25lO 

4 

55 

9979 

..28 

•'•77 

.  126 

•  i74 

.223 

4 

56 

2559 

26o9 

659 

2709 

2758 

2808 

3 

56 

9.76o272 

0320 

o369 

0418 

o466 

o5i5 

3 

5? 

2858 

2007 

957 

3007 

3o56 

3io6 

2 

57 

o564 

0612 

0661 

0710 

o758 

0807 

2 

58 

3i56 

3206 

3255 

33o5 

3355 

34o4 

I 

58 

o856 

o9o4 

o953 

1  002 

io5o 

1099 

I 

,  59 

.3454 

35o4 

3553 

36o3 

3653 

3702 

O 

59 

n48 

n96 

1245 

I293 

1  342 

1391 

O 

60" 

50" 

40" 

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20" 

10" 

d 

60"     50"  |  40" 

30" 

20" 

10" 

. 

Co-tangent  of  61  Degrees. 

•9 

g 

Co-tangent  of  60  Degrees. 

i 

P  Part*  l"   2"   3//   4//   5"   6"   7//   8"   9" 

.  (  1"  2"  3"  4"  5"  6"  7"  8"  9" 

irl$  5  10  15  20  25  30  35  40  45      IIL}  5   10  15  20  25  29  34  39  44 

54 


LOGARITHMIC    SINES. 


1 

Sine  of  30  Degrees. 

* 

Sine  of  3  1  Degrees. 

s 

0" 

10" 

20"  1  30"  |  40" 

50" 

§ 

0"    |  10" 

20" 

30" 

40" 

50" 

0 

9.69897o 

9oo6 

9043  9079  9116 

9l52 

59 

o 

9.7n839 

i874 

I9o9 

1944 

I979 

2Ol4 

59 

I 

9189 

9225 

9262  9298:9334 

937I  58 

i 

2o5o 

2o85 

2120 

2i55 

2I90 

2225 

58 

2 

9407 

9444 

94809517:9553 

958957 

2 

2260 

2295 

2330 

2365 

240O 

2434 

57 

r 

9626 

9662 

969997359771 

9808 

56 

3 

2469 

25o4 

2539 

2574 

26o9 

2644 

56 

4 

9844 

988o 

99i79953999o 

.,26 

55 

4 

2679 

27l4 

2749 

2784 

28i9 

2854 

55 

i 

9.700062 

oo99 

oi35  oi7i 

0208 

0244 

54 

5 

2889 

2924 

2959 

2994 

3o29 

3o63 

54 

6 

0280 

0317 

o353o389 

0425 

0462 

53 

6 

3o98 

3i33 

3i68 

32o3 

3238 

3273 

53 

7 

0498 

o534 

o57i  o6o7 

o643 

0680 

52 

7 

33o8 

3343 

3377 

34i2 

3447 

3482 

52 

8 

0716 

0752 

07880825 

0861 

o897 

5i 

8 

35i7 

3552 

3587 

362i 

3656 

369i 

5i 

9 

o933 

0970  1006  1042 

1078 

in5 

5o 

9 

3726 

376i 

3W6 

383o 

3865 

3900 

5o 

IO 

9.701151 

1187 

1223  I25g 

1296 

i332 

49 

IO 

9.7i3935 

397o 

4oo5 

4039 

4074 

4109 

49 

ii 

i368 

i4o4 

i44o  i477 

i5i3 

i549 

48 

ii 

4i44 

4i79 

4213 

4248 

4283 

43i8 

48 

12 

i585 

1621 

i658  i694 

1730 

1-766 

47 

12 

4352 

4387 

4422 

4457 

449i 

4526 

47 

i3 

1802 

i838 

i874  i9n 

1947 

i983 

46 

i3 

456i 

4596 

463o 

4665 

4700 

4735 

46 

i4 

2019 

2o55 

2O9I  2I27 

2164 

22OO 

45 

i4 

4769 

48o4 

4839 

4873 

49o8 

4943 

45 

i5 

2236 

2272 

23o8-2344 

238o 

2416 

44 

i5 

4978 

5012 

5o47 

5o82 

5n6 

5i5i 

44 

16 

2452 

2488 

25242561 

2597 

2633 

43 

16 

5i86 

522O 

5255 

5290 

5324 

5359 

43 

17 

2669 

27o5  2741^777 

28i3 

2849 

42 

'7 

5394 

5428 

5463 

5498 

5532 

5567 

42 

18 

2885 

292I 

2957  2993 

3029 

3o65 

4i 

18 

56o2 

5636 

567i 

57o5 

574o 

5775 

4i 

i9 

3ioi 

3i37 

3173  3209 

3245 

3281 

4o 

i9 

58o9 

5844 

587f 

59i3 

5948 

5982 

4o 

20 

9.7o33I7 

3353 

3389!3425 

346i 

3497 

39 

20 

9.  716017 

6o5i 

6086 

6121 

6i55 

6190 

39 

21 

3533 

3569 

36o5  364i 

3677 

37i3 

38 

21 

6224 

6259 

6293 

6328 

6362 

6397 

38 

22 

3749 

3784 

38203856 

3892 

3928 

37 

22 

6432 

6466 

65oi 

6535 

657o 

66o4 

37 

23 

3964 

4ooo 

4o36j4o72 

4io8 

4i44 

36 

23 

6639 

6673 

67o8 

6742 

6777 

6811 

36 

24 

4i79 

42i5 

425i4287 

4323 

4359 

35 

24 

6846 

6880 

69i5 

6949 

6984 

7018 

35 

25 

4395 

443i 

4466j45o2 

4538 

4574 

34 

25 

7o53 

7o87 

7I22 

7i56 

7i9i 

7225 

34 

26 

46io 

4682'47i7 

4753 

4789 

33 

26 

7259 

7294 

7328 

7363 

7397 

7432 

33 

27 

4825 

486i'4896|4932 

4968 

5oo4 

32 

27 

7466 

7535 

7569 

7604 

7638 

32 

28 

5o4o 

5075 

5ni 

5i47 

5i83 

52I9 

3i 

28 

7673 

77°7 

774i 

7776 

7810 

7844 

3i 

29 

5254 

5290 

5326 

5362 

5397 

5433 

3o 

29 

7879 

79i3 

7948 

7982 

8016 

8o5i 

3o 

3o 

9.7o5469 

55o5 

554o 

5576 

56i2 

5648 

29 

3o 

9.  718085 

8n9 

8i54 

8188 

8223 

8257 

29 

3i 

5683 

5719  5755 

579° 

5826 

5862 

28 

3i 

829I 

8326 

836o 

8394 

8429 

8463 

28 

32 

5898 

5933 

5969 

6oo5 

6o4o 

6o76 

27 

32 

8497 

853i 

8566 

8600 

8634 

8669 

27 

33 

6112 

61476183 

6219 

6254 

629o 

26 

33 

87o3 

8737 

8772 

8806 

884o 

8874 

26 

34 

6326 

636i 

6397 

6433 

6468 

65o4 

25 

34 

89o9 

8943 

8977 

9on 

9o46 

9080 

25 

35 

6539 

6575 

6611 

6646 

6682 

67i8 

24 

35 

9n4 

9i48 

9i83 

93I7 

925l 

9285 

24 

36 

6753 

6789  6824 

6860 

6895 

693i 

23 

36 

9320 

9354 

9388 

9422 

9456 

9491 

23 

37 

6967 

7002 

7o38 

7o73 

7109 

7i45 

22 

37 

9525 

9559 

9593 

9627 

9662 

9696 

22 

38 

7180 

7216  725i 

7287 

7322 

7358 

21 

38 

973o 

9764 

979s 

9833 

9867 

9901 

21 

39 

7393 

7429 

7464 

7535 

757i 

20 

39 

9935 

9969 

...3 

..38 

..72 

.  106 

2O 

4o 

9.  707606 

7642 

7677 

77i3 

7748 

7784 

I9 

4o 

9.  720140 

oi74 

0208 

0242 

0276 

o3n 

'9 

4i 

7819 

7855 

789o 

7926 

7961 

7997 

18 

4i 

o345 

o379 

o4i3 

o447 

o48i 

o5i5 

18 

42 

8o32 

8068 

8io3 

8i39 

8174 

8210 

i7 

42 

o549 

o583 

0617 

o652 

0686 

0720 

17 

43 

8245 

8^80  83i6 

835i 

8387 

8422 

16 

43 

0754 

o788 

0822 

o856 

0890 

0924 

16 

44 

8458 

8^3 

8528 

8564 

8599 

8635 

i5 

44 

o958 

0992 

1026 

1060 

1094 

1128 

i5 

45 

8670 

87o5 

874i 

8776 

8811 

8847 

i4 

45 

1162 

1  196 

1230 

1264 

1298 

i332 

i4 

46 

8882 

8918 

8953 

8988 

9024 

9o59 

i3 

46 

1  366 

i4oo 

i434 

1  468 

1  602 

i536 

i3 

47 

9o94 

9i3o  9i65 

9200 

9236  9271 

12 

47 

1570 

i6o4 

i638 

l672 

1706 

i74o 

12 

48 

93o6 

9342 

9377 

9412 

9448  9483 

II 

48 

i774 

1808 

1842 

i876 

1910 

1944 

II 

49 

95i8 

95539589 

9624 

9659  9695 

IO 

49 

i978 

2012 

2046 

2080 

2114 

2148 

10 

5o 

9.7o973o 

9765  98oo 

9836 

9871  9906 

9 

5o 

9.  722181 

22l5 

2249 

2283 

2317 

235i 

9 

5i 

994i 

9977 

.  .  12 

..47 

..82  .118 

8 

5i 

2385 

24l9 

2453 

2487 

2520 

2554 

8 

52 

9.7ioi53 

01880223 

0259 

0294  0329 

7 

52 

2588 

2622 

2656 

269o 

2724 

2757 

7 

53 

o364 

o399  o435 

0470 

o5o5  o54o 

6 

53 

279I 

2825 

28592893 

2927 

2960 

6 

54 

o575 

06  1  1 

o646 

0681 

0716  0751 

5 

54 

2.994 

3028^062  3o96  3i3o:3i63 

5 

55 

0786 

08220857 

0892 

0927  0962 

4 

55 

3i97  323il3265:3299!3332  3366 

4 

56 

°997 

I032! 

1067 

no3 

n38  n73 

3 

56 

34oo  3434  3468;35oi  3535  3569 

3 

57 

1208 

1243 

1278 

i3i3 

i348  i383 

2 

57 

36o33636367o37o43738377i  2 

58 

i4i9 

i454 

1489 

i524 

i559  i594 

I 

58 

38o5:38393873  39o6  394o3974  i 

59 

i629 

1664 

1699 

1734 

1769  1  8o4 

O 

59 

4oo7  4o4i  4075  4io9  4i42  4176  o 

60" 

50" 

40"  |  30"  |  20"  i  10" 

a 

60"     50"  .  40"   30"   20"   10"  1  . 

Co-sine  of  59  Degrees. 

•fl 

Co-sine  of  58  Degrees.     '£ 

.  (  1"  2"  3"  4"  5"  6"  7"  8"  9"   „  „  J  1"  2"  3"  4"  5"  6"  7"  8"  9" 

"{  4   7  11 

14  18  21  25  29  32        \  3   7  10  14  17  21  24  27  31 

LOGARITHMIC    TANGENTS. 


.5 

Tangent  of  30  Degrees. 

Jj 

Tangent  of  3  1  Degrees. 

0" 

10" 

20" 

30" 

40" 

50" 

0" 

10" 

20" 

30" 

40" 

50" 

0 

9.  -761439 

i486 

i537 

i585 

i634 

1682 

59 

o 

9.  778774 

8821 

8869 

89i7 

8964 

9OI2 

59 

i 

I73i 

1-780 

1828 

1877 

I925 

i974 

58 

i 

9060 

9io8 

9i55 

9203 

925l 

9298 

58 

2 

8O22 

20-71 

2I2O 

2168 

2217 

2266 

57 

2 

9346 

9394 

944i 

9489 

9537 

9584 

57 

3 

23l4 

2363 

2411 

2460 

25o8 

2557 

56 

3 

9632 

9679 

9727 

9775 

9822 

987o 

56 

4 

2606 

2654 

27o3 

2751 

2800 

2848 

55 

4 

99I8 

9965 

..61 

.108 

.i56 

55 

5 

2897 

2945 

2994 

3o43 

3o9i 

3i4o 

54 

5 

9.  780203 

025l 

0299 

o346 

o394 

o44i 

54 

6 

3i88 

3237 

3285 

3334 

3382 

343i 

53 

6 

o489 

o537 

o584 

o632 

o679 

0727 

53 

7 

3479 

3528 

3576 

3625 

3673 

3722 

52 

7 

0775 

0822 

o87o 

o9i7 

o965 

ioi3 

52 

8 

377o 

38i9 

3867 

39i6 

3964 

4oi3 

5i 

8 

1060 

1108 

n55 

1203 

I25o 

1298 

5i 

9 

4o6i 

4no 

4i58 

4207 

4255 

43o4 

5o 

9 

1  346 

i393 

i44i 

i488 

i536 

i583 

5o 

10 

9.  764352 

44oo 

4449 

4497 

4546 

4594 

49 

IO 

9.  781631 

i678 

1-726 

i774 

1821 

1869 

49 

II 

4643 

469i 

474o 

4788 

4836 

4885 

48 

ii 

i9i6 

i964 

2OII 

2o59 

2106 

2  I  54 

48 

12 

4933 

4982 

5o3o 

5079 

5127 

5i75 

47 

12 

22OI 

2249 

2296 

2344 

239I 

2439 

47 

i3 

5224 

5272 

532i 

5369 

54i8 

5466 

46 

i3 

2486 

2534 

258i 

2629 

26-76 

2724 

46 

i4 

55i4 

5563 

56n 

566o 

57o8 

5756 

45 

i4 

2771 

28l9 

2866 

29i4 

2961 

3OO9 

45 

i5 

58o5 

5853 

5901 

SgSo 

5998 

6o47 

44 

i5 

3o56 

3io4 

3i5i 

3i99 

3246 

3294 

44 

16 

6095 

6i43 

6192 

6240 

6288 

6337 

43 

16 

334i 

3388 

3436 

3483 

353i 

3578 

43 

i7 

6385 

6433 

6482 

653o 

6578 

6627 

42 

'7 

3626 

3673 

372I 

3768 

38i6 

3863 

42 

18 

6675 

6723 

6772 

6820 

6868 

691-7 

4i 

18 

39io 

3958 

4oo5 

4o53 

4ioo 

4i48 

4i 

19 

6965 

7oi3 

-7062 

7110 

7i58 

7207 

4o 

19 

4i95 

4242 

4290 

4337 

4385 

4432 

4o 

20 

9.767255 

73o3 

7352 

74oo 

7448 

7496 

39 

20 

9.784479 

4527 

4574 

4622 

4669 

47i6 

39 

21 

7545 

7593 

764i 

7690 

7738 

7786 

38 

21 

4764 

48u 

4859 

49o6 

4953 

5ooi 

38 

22 

7834 

7883 

793i 

7919 

8027 

80-76 

37 

22 

5o48 

5o95 

5i43 

5i9o 

5238 

5285 

37 

23 

8124 

81-72 

8221 

8269 

83i7 

8365 

36 

23 

5332 

538o 

5427 

5474 

5522 

5569 

36 

24 

84i4 

8462 

85io 

8558 

8606 

8655 

35 

24 

56i6 

5664 

57n 

5758 

58o6 

5853 

35 

25 

87o3 

875i 

8799 

8848 

8896 

8944 

34 

25 

59oo 

5948 

5995 

6042 

6090 

6i37 

34 

26 

8992 

9o4o 

9o89 

9i37 

9i85 

9233 

33 

26 

6i84 

6232 

6279 

6326 

6374 

6421 

33 

27 

9281 

933o 

9378 

9426 

9474 

9522 

32 

27 

6468 

65i6 

6563 

6610 

6657 

67o5 

32 

28 

957i 

96i9 

9667 

97i5 

9763 

9811 

3i 

28 

6752 

6799 

6847 

6894 

6941 

6988 

3i 

29 

9860 

99o8 

9956 

...4 

..52 

.  100 

3o 

29 

7o36 

7o83 

7i3o 

7178 

7225 

7272 

3o 

3o 

9.77oi48 

oi97 

0245 

0293 

o34i 

o389 

29 

3o 

9.7873I9 

7367 

74i4 

746  1 

75o8 

7556 

29' 

3i 

o437 

o485 

o534 

o582 

o63o 

06-78 

28 

3i 

76o3 

765o 

7697 

7745 

7792 

7839 

28 

32 

0-726 

o774 

0822 

0870 

o9i9 

096-7 

27 

32 

-7886 

7934 

798i 

8028 

8o75 

8122 

27 

33 

ioi5 

io63 

1  1  1  1 

n59 

1207 

1255 

26 

33 

81-70 

821-7 

8264 

83n 

8359 

84o6 

26 

34 

i3o3 

i35i 

i399 

i448 

i496 

1  544 

25 

34 

8453 

85oo 

8547 

8595 

8642 

8689 

25 

35 

i592 

i64o 

1688 

1736 

1784 

i832 

24 

35 

8736 

8783 

883o 

8878 

8925 

8972 

24 

36 

1880 

I928 

i976 

2024 

2072 

2I2O 

23 

36 

9oi9 

9o66 

9n4 

9161 

92o8 

9255 

23 

37 

2168 

2216 

2264 

23l2 

236i 

2409 

22 

37 

93o2 

9349 

9397 

9444 

949i 

9538 

22 

38 

2457 

25o5 

2553 

2601 

2649 

2697 

21 

38 

9585 

9632 

9679 

9727 

9774 

982I 

21 

QQ 

2745 

2703 

2841 

2889 

2O37 

2985 

2O 

3o 

9868 

ooi  5 

0062 

57 

.  i  o4 

2O 

4o 

9.773o33 

/vw 

3o8i 

3i29 

3i77 

7   / 

3225 

3273 

J9 

/ 

4o 

9.79oi5i 

vvx^ 
oi98 

fl 
0245 

O292 

o339 

o386 

19 

4i 

332i 

3369 

3417 

3465 

35i2 

356o 

18 

4i 

o434 

o48i 

o528 

o575 

0622 

o669 

18 

42 

36o8 

3656 

3704 

3752 

38oo 

3848 

'7 

42 

O7i6 

o763 

0810 

o857 

ogoS 

O952 

17 

43 

3896 

3944 

3992 

4o4o 

4o88 

4i36 

16 

43 

°999 

io46 

1093 

n4o 

1187 

1234 

16 

44 

4i84 

4232 

4280 

4328 

4375 

4423 

i5 

44 

1281 

i328 

!375 

l422 

1469 

i5i6 

i5 

45 

447i 

45i9 

4567 

46i5 

4663 

47n 

i4 

45 

i563 

1611 

i658 

I7o5 

I752 

i799 

i4 

46 

4759 

48o7 

4855 

4902 

495o 

4998 

i3 

46 

1  846 

i893 

1940 

i987 

2o34 

2081 

i3 

47 

5o46 

5o94 

5i42 

5i9o 

5238 

5286 

12 

47 

2128 

2I75 

2222 

2269 

23i6 

2363 

12 

48 

5333 

538i 

5429 

5477 

5525 

5573 

II 

48 

2410 

2457 

25o4 

255i 

2598 

2645 

II 

49 

562! 

5668 

5716 

5764 

58i2 

586o 

IO 

49 

2692 

2739 

2786 

2833 

2880 

2927 

IO 

5o 

9.  -7-75908 

5956 

6oo3 

6o5i 

6o99 

6i47 

9 

5o 

9-792974 

3O2I 

3o68 

3n5 

3i62 

3209 

9 

5i 

6195 

6243 

6290 

6338 

6386 

6434 

8 

5i 

3256 

33o3 

335o 

3397 

3444 

349i 

8 

52 

6482 

6529 

6577 

6625 

6673 

672I 

7 

52 

3538 

3585 

3632 

3679 

3726:3773 

7 

53 

6768 

6816 

6864 

69I2 

6960 

7°°7 

6 

53 

38i9 

3866 

39i3 

396o 

4oo7  4o54 

6 

54 

7o55 

7io3 

7i5i 

7i99 

7246 

7294 

5 

54 

4ioi 

4i48 

4i95 

4242 

42894336 

5 

55 

7342 

739o 

7437 

7485 

7533 

758i 

4 

55 

4383 

443o 

4 

56 

-7628 

7676 

7724 

7772 

78i9 

7867 

3 

56 

4664 

47n 

4758 

48o5  4852  4899 

3 

57 

79i5 

7963 

8010 

8o58 

8106 

8i54 

2 

57 

4946 

4992  5o39 

5o865i335i8o 

2 

58 

8201 

8249 

8297 

8344 

8392 

844o 

I 

58 

5227 

5274532i  5367!54i4546i 

I 

59 

8488 

85358583 

863i 

8678 

8726 

O 

59 

55o8  5555  56o2  5649 

5696  5742 

O 

W     50"   40" 

30"   20" 

10" 

~T~ 

60"     50"  )  40"  i  30" 

20"  ,  10" 

G 

Co-tangent  of  59  Degrees. 

S3 

Co-tangent  of  58  Degrees. 

1 

P  Part*  l"  ~"  3"  4"  5"  6"  7"  8"  9" 

C  l"  2"  3"  4"  5"  6"  7"  8"  9" 

\  5  10  14  19  24  29  34  39  43 

irt\  5  9  14  19  24  28  33  38  43 

bfl 


LOGARITHMIC    SINES. 


_g 

Sine  of  32  Degrees. 

.s 

Sine  of  33  Degrees 

9 

0 

10" 

20" 

30" 

40" 

50" 

2 

0"     10"   20"  |  30".   40" 

50" 

o 

9.724210 

4243 

4277:4311 

4344 

4378 

59 

0 

9.736io9  6i4i  6i74  6206 

6238 

627I 

59 

i 

44i2 

4445 

447945i3 

4546 

458o 

58 

I 

63o3  6336  636864oo 

6433 

6465 

58 

2 

46i4 

4647 

468i  47i5 

4748 

4782 

57 

2 

6498653066626696 

6627 

6659 

57 

3 

48i6 

4849 

4883  49i7 

495o 

4984 

56 

3 

6692,6-724  6757|6789 

6821 

6854 

56 

4 

5oi7 

5o5i 

5o85' 

5n8 

5i52 

5i85 

55 

4 

6886'69i8;695iJ6983 

7oi5 

7o48 

55 

5 

5219 

5253 

5286 

5320 

5353 

5387 

54 

5 

•7080  7112  7145)7177 

7209 

7241 

54 

6 

5420 

5454 

5488 

552i 

5555 

5588 

53 

6 

7274 

73o67338|737i 

74o3 

7435 

33 

7 

5622 

5655 

5689 

5722 

5756 

5789 

52 

7 

7467 

75oo 

76327664 

7597 

7629 

52 

8 
9 

10 

5823 
6024 
9.726225 

5856 
6o57 
6258 

589o5923 
6091  6124 
6292  6325 

5957 
6i58 
6359 

599o 
6i9i 
6392 

5i 
5o 
49 

8 
9 

10 

766i 
7855 
9.788048 

7693772617768 
788779197961 

8o8o8ii28i45 

779° 
7983 
8i77 

7822 
8016 
8209 

Si 

5o 

49 

ii 

6426 

6459 

6493  6526 

656o 

6593 

48 

ii 

8241 

8273 

83o68338 

837o 

8402 

48 

12 

6626 

6660 

6693  6727 

6760 

6704 

47 

12 

8434 

84668499|853i 

8563 

8595 

47 

i3 

6827 

6860 

6894  6927 

6961 

6994 

46 

i3 

86278659 

8692 

8724 

8756 

8788 

46 

i4 

7027 

7061 

7094 

7128 

7161 

7i94 

45 

i4 

88208852 

8884 

89i78949 

898i 

45 

i5 

7228 

7261 

7294 

7328 

736i 

7394 

44 

i5 

9013  9045 

9°77 

9io99i4i 

9i73 

44 

16 

7428 

746  1 

7494 

7528 

756i 

7594 

43 

16 

9206 

9238 

9270 

93o2  9334 

9366 

43 

17 

7628 

7661 

7694 

7728 

7761 

7794 

42 

J7 

•9398 

943o 

9462 

9494 

95269558 

42 

18 

7828 

7861 

7894 

7928 

7961 

7994 

4i 

18 

959o 

9622 

9654 

968? 

97i9 

975! 

4i 

I9 

8027 

8061 

80948127 

8161 

8i94 

4o 

J9 

9783 

98i5 

9847 

9879 

99n 

9943 

4o 

20 

9.728227 

8260 

82948327 

836o 

8393 

39 

20 

9.739975 

...7 

..39 

..7i 

,io3 

.i35 

39 

21 

8427 

846o 

84938526 

856o8593 

38 

21 

9.  740167 

oi99 

023l 

0263 

O295 

o327 

38 

22 

8626 

8659 

8692 

8726 

8759!8792 

37 

22 

o359 

o39i 

o423 

o455 

o487 

o5i9 

3? 

23 

8825 

8858 

8892 

8925 

89588991 

36 

23 

o55o 

o582 

06  1  4 

o646 

o678 

07IO 

36 

24 
25 

9024 
9223 

9o58 

9257 

9091 
9290 

9I24 

9323 

915719190 
93569389 

35 

34 

24 
25 

0742 
o934 

0774 
o966 

0806 

°997 

o838 

I029 

o87o 
1061 

O902 

io93 

35 
34 

26 

9422 

9455 

9489  9522 

95559588 

33 

26 

1125 

1  157 

n89 

1221 

1253 

1284 

33 

27 

9621 

9654 

96879720 

9753 

9787 

32 

27 

i3i6 

1  348 

i38o 

1412 

1  444 

i476 

32 

28 

9820 

9853 

9886  9919 

9952 

9985 

3i 

28 

i5o8 

i539 

1671 

i6o3 

i635 

i667 

3i 

29  9.730018 

oo5i 

oo84 

0117 

oi5o 

oi83 

3o 

29 

i699 

1730 

1762 

i794 

1826 

i858  3o 

*3o  9.730217 

025o 

0283  o3i6 

0349  o382 

29 

3o 

9.74i889 

I92I 

i953 

i985 

20I7 

2049 

29 

3i 

o4i5 

o448 

0481 

o5i4 

o547  °58o 

28 

3i 

2080 

2112 

2i44 

2I76 

22O7 

2239  28 

32 

o6i3 

0646 

06790712 

o745 

0778 

27 

32 

2271 

23o3 

2335 

2366 

2398 

243o 

27 

33 

0811 

o844 

0877 

o9io 

o943 

o976 

26 

33 

2462 

2493 

2525 

2557 

2589 

2620 

26 

34 

1009 

1042 

1075 

1  1  08 

n4i 

n73 

25 

34 

2652 

2684 

27l5 

2747 

2779 

28  1  i 

25 

35 

1206 

1239 

1272 

i3o5 

i338 

i37i 

24 

35 

2842 

28-74 

29o6 

2937 

2969 

3ooi 

24 

36 

i4o4 

i437 

1470 

i5o3 

i536 

i569 

23 

36 

3o33 

3o64 

3o96 

3128 

3i59 

3i9i 

23 

37 

1602 

1  634 

1667 

1700 

i733 

1766 

22 

37 

3223 

3254 

3286 

33i83349 

338i 

22 

38 

1799 

i832 

i865 

i897 

I93o 

i963 

21 

38 

34i3 

3444 

3476 

35o8  3539 

357i 

21 

39    1996 

2029 

2062 

2095 

2127 

2160 

20 

39 

36o2 

3634 

3666 

3697 

3729 

376i 

20 

409.732193 

2226 

2259  2292 

2325 

2357 

I9 

4o 

9.743792 

3824 

3855 

3887 

39i9 

395o 

J9 

4i 

2390 

2423 

2456  2489 

2521 

2554 

18 

4i 

3982 

4oi3 

4o45 

4o77 

4io8 

4i4o 

18 

42 

2587 

2620 

2653  2685 

2718 

2?5l 

17 

42 

4i7i 

4203 

4234 

4266 

429-7 

4329 

17 

43 

2784 

2816 

2849  2882 

29l5 

2948 

16 

43 

436i 

4392 

4424 

4455 

4487 

45i8 

16 

44 

2980 

3oi3 

3o46  3o79 

3in 

3i44 

i5 

44 

455o 

458i 

46i3 

4644 

4676 

47o7 

i5 

45 

3i77 

3210 

8242 

3275 

33o8 

334o 

i4 

45 

4739 

477o 

4802 

4833 

4865 

4896 

i4 

46 

3373 

34o6 

34393471 

35o4 

3537 

i3 

46 

4928 

4959 

499i 

5022 

5o54 

5o85 

i3 

47 
48 

49 

3569 
3765 
396i 

36o2 
3798 
3994 

3635  36673700 
383i  3863|3896 
4027  4o59  4092 

3733 
3929 

4i25 

12 
II 
IO 

47 
48 

49 

5n7 
53o6 
5494 

5i48 
5337 
5526 

5i8o 
5369 
5557 

5211 
5400 

5589 

5243 
543i 
5620 

5274 
5463 
565i 

12 
II 
IO 

5o 

9.734157 

4i9o 

4222 

4255 

4288 

4320 

9 

5o 

9.745683 

57i4|5746 

5777 

58o8 

584o 

9 

5i 

4353 

4386 

44i8 

445  1 

4483 

45i6 

8 

5i 

587i 

69036934 

5965 

5997 

6028 

8 

52 

4549 

458i 

46i4 

4646 

4679 

47n 

7 

52 

6060 

6091  6122 

6  1  54  6  1  85 

6216 

7 

53 

4744 

4?77 

4809 

4842 

4874 

49o7 

6 

53 

6248!6279!63io 

63426373 

64o4 

6 

54 

4939 

4972 

5oo4 

5o37  5069 

5l02 

5 

54 

6436  6467  6498 

653o656i 

6592 

5 

55 

5i35 

5i67 

52OO 

52325265 

5297 

4 

55 

6624  6655  6686 

67i86749 

678o 

4 

56 

533o 

5362 

5395 

5427 

546o 

5492 

3 

56 

68i2'6843 

6874 

69o5 

6937 

6968  3 

57 

5525 

5557 

559o 

5622 

5655 

5687 

2 

57 

6999!7o3i 

-7062 

7o93 

•7124 

7i56 

2 

58 

57i9 

5752 

5784 

58i7 

5849 

5882 

I 

58 

71877218 

7249 

728lJ73l2 

7343 

I 

59 

5gi4 

5947 

5979 

601  1  6o44 

6o76 

O 

59 

7374|74o6 

7437  7468)7499  753o 

O 

60" 

50" 

40' 

30"   20" 

10" 

B 

60"     50"   40"   30"   20"   10" 

a 

Co-sine  of  57 

Degrees. 

i 

Co-sine  of  56  Degrees. 

i 

.<  1"  2"  3"  4" 

5"  6"  7"  8"  9" 

p  p   C  1"  2"  3"  4"  5"  6"  7"  8"  9" 

P.PMtj  3  7  10  13 

17  20  23  26  30 

1  n\  3   6  10  13  16  19  22  25  29 

LOGARITHMIC    TANGENTS. 


rl 

Tangent  of  32  Degrees. 

d 

Tangent  of  33  Degrees. 

* 

0" 

10" 

20"   30" 

40" 

50" 

a 

0" 

10" 

20" 

30"   40" 

00" 

o 

9-795789 

5836 

5883593o 

5977 

6023 

59 

o 

9.8i25i7 

2563 

2610 

2656 

27O2 

2748 

59 

I 

6070 

6n7 

616416211 

6258 

63o4 

58 

i 

2794 

2840 

2886 

2932 

2978 

3o24 

58 

6 

635i 

6398 

6445 

6492 

6539 

6585 

57 

2 

3070 

3n6 

3i63 

3209 

3255 

33oi 

57 

3 

6632 

6679 

6726 

6773 

68i9 

6866 

56 

3 

3347 

3393 

3439 

3485 

353i 

3577 

56 

4 

69i3 

696o 

7oo7 

7o53 

7100 

7i47 

55 

4 

3623 

3669 

37i5 

376i 

38o7 

3853 

55 

5 

7i94 

724l 

7287 

7334 

738i 

7428 

54 

5 

3899 

3945 

399i 

4o37 

4o83 

4i29 

54 

6 

7474 

752I 

7568 

76i5 

7662 

77o8 

53 

6 

4176 

4222 

4268 

43i4 

436o 

44o6 

53 

7 

7755 

7802 

7849 

7895 

7942 

7989 

52 

7 

4452 

4498 

4544 

4590 

4636 

4682 

52 

8 

8o36 

8082 

8i29 

8176 

8223 

8269 

5i 

8 

4728 

4774 

4820 

4866 

49I2 

4958 

5i 

9 

83i6 

8363 

84o9 

8456 

85o3 

855o 

5o 

9 

5oo4 

5o5o 

5o96 

5i42 

5i88 

5  2  34 

5o 

10 

9.798596 

8643 

8690 

8737 

8783 

883o 

49 

10 

9.8i528o 

5326 

5371 

5417 

5463 

55o9 

49 

ii 

8877 

8923 

897o 

9017 

9o63 

9no 

48 

ii 

5555 

56oi 

5647 

5693 

5739 

5785 

48 

12 

9i57 

9204 

925o 

9297 

9344 

939o 

47 

12 

583i 

5877 

5923 

5969 

6oi5 

6061 

47 

i3 

9437 

9484 

953o 

9577 

9624 

967o 

46 

i3 

6107 

6i53 

6i99 

6245 

629I 

6336 

46 

i4 

97i7 

9764 

9810 

9857 

99o4 

995o 

45 

i4 

6382 

6428 

6474 

6520 

6566 

6612 

45 

i5 

9997 

..44 

..90 

.i37 

.184 

.230 

44 

i5 

6658 

6704 

6750 

6796 

6842 

6888 

44 

16 

9.8oo277 

0324 

o37o 

o463 

o5io 

43 

16 

6933 

6979 

7025 

7071 

7117 

7i63 

43 

I7 

o557 

o6o3 

o65o 

o697 

o743 

°79° 

42 

17 

7209 

7255 

73oi 

7347 

7392 

7438 

42 

18 

o836 

o883 

ogSo 

o976 

1023 

I07O 

4i 

18 

7484 

753o 

7576 

7622 

7668 

7714 

4i 

19 

1116 

n63 

1209 

1256 

i3o3 

1  349 

4o 

i9 

7759 

7805 

785i 

7897 

7943 

7989 

4o 

20 

9.8oi396 

1442 

1489 

i535 

i582 

1629 

39 

20 

9.8i8o35 

8081 

8126 

8172 

8218 

8264 

39 

21 

1675 

1722 

1768 

i8i5 

1862 

1908 

38 

21 

83io 

8356 

8402 

8447 

8493 

8539 

38 

22 

i955 

2OOI 

2048 

so94 

2l4l 

2l87 

37 

22 

8585 

863i 

8677 

8722 

8768 

8814 

37 

23 

2234 

228l 

2327 

2374 

2420 

2467 

36 

23 

8860 

89o6 

8952 

8997 

9o43 

9o89 

36 

24 

25i3 

256o 

2606 

2653 

2699 

2746 

35 

24 

9i35 

9i8i 

9226 

9272 

93i8 

9364 

35 

25 

2792 

2839 

2886 

2932 

2979 

3o25 

34 

25 

94io 

9455 

95oi 

9547 

9593 

9639 

34 

26 

3072 

3n8 

3i65 

3211 

3258 

33o4 

33 

26 

9684 

973o 

9776 

9822 

9868 

99i3 

33 

27 

335i 

3397 

3444 

349o 

3537 

3583 

32 

27 

9959 

..96 

.142 

.188 

32 

28 

363o 

3676 

3723 

3769 

38i6 

3862 

3i 

28 

9.820234 

0280 

o325 

o37i 

o4i7 

o463 

3i 

29 

39o9 

3955 

4ooi 

4o48 

4o94 

4i4i 

3o 

29 

o5o8 

o554 

0600 

o646 

o69i 

o737 

3o 

3o 

9.8o4i87 

4234 

4280 

4327 

4373 

4420 

29 

3o 

9:820783 

o829 

o874 

0920 

0966 

1012 

29 

•  3i 

4466 

45i3 

4559 

46o5 

4652 

4698 

28 

3i 

1057 

no3 

n49 

iigS 

1240 

1286 

28 

32 

4745 

479i 

4838 

4884 

493o 

4977 

27 

32 

i332 

i377 

1423 

1469 

i5i5 

i56o 

27 

33 

5o23 

5070 

5n6 

5i63 

5209 

5255 

26 

33 

1606 

i652 

i697 

1743 

1789 

i835 

26 

34 

5302 

5348 

5395 

544i 

5487 

5534 

25 

34 

1880 

I926 

I972 

2017 

ao63 

2I09 

25 

35 

558o 

5627 

5673 

57i9 

5766 

58i2 

24 

35 

2i54 

22OO 

2246 

2292 

•-337 

2383 

24 

36 

5859 

59o5 

595i 

5998 

6o44 

6091 

23 

36 

2429 

2474 

2520 

2566 

2611 

2657 

23 

37 

6i37 

6i83 

623o 

6276 

6322 

6369 

22 

37 

2703 

2748 

2794 

2840 

2885 

293i 

22 

38 

64i5 

6462 

65o8 

6554 

6601 

6647 

21 

38 

2977 

3022 

3o68 

3n4 

3i59 

32o5 

21 

39 

6693 

6740 

6786 

6832 

6879 

6925 

20 

39 

325i 

3296 

3342 

3387 

3433 

3479 

20 

4o 

9  806971 

7018 

7064 

7IIO 

7i57 

7203 

I9 

4o 

9.  823524 

357o 

36i6 

366i 

37o7 

3753 

19 

4i 

7249 

7296 

7342 

7388 

7435 

748i 

18 

4i 

3798 

3844 

3889 

3935 

398i 

4026 

18 

42 

7527 

7574 

7620 

7666 

77i3 

7759 

17 

42 

4072 

4u7 

4i63 

4209 

4254 

43oo 

17 

43 

78o5 

785i 

7898 

7944 

799° 

8o37 

16 

43 

4345 

439i 

44?7 

4482 

4528 

4573 

16 

44 

8o83 

8129 

8176 

8222 

8268 

83i4 

i5 

44 

46i9 

4665 

4710 

4756 

48oi 

4847 

i5 

45 

836i 

84o7 

8453 

8499 

8546 

8592 

i4 

45 

4893 

4938 

4984 

5029 

5o75 

5l2O 

i4 

46 

8638 

8685 

873i 

8777 

88a3 

887o 

i3 

46 

5i66 

5212 

5257 

53o3 

5348 

5394 

i3 

47 

89i6 

8962 

9008 

9o55 

9ioi 

9147 

12 

47 

54>9 

5485 

553i 

5576 

5622 

5667 

12 

48 

•  9i93 

9240 

9286 

9332 

9378 

9424 

II 

48 

57i3 

5758 

58o4 

5849 

5895 

594o 

II 

49 

947i 

95i7 

9563 

96o9 

9656 

9702 

IO 

49 

5986 

6o32 

6077 

6i23 

6168 

6214 

IO 

5o 

9.8o9748 

9794 

9840 

9887 

9933 

9979 

9 

5o 

9.826259 

63o5 

635o 

6396 

644i 

648  7 

9 

5i 

9.  810025 

0071 

0118 

0164 

0210 

0256 

8 

5i 

6532 

6578 

6623 

6669 

67i4 

6760 

8 

52 

o3o2 

o349 

o395 

o44i 

o487 

o533 

7 

52 

68o5 

685i 

6896 

6942 

6987 

7o33 

7 

53 

o58o 

0626 

0672 

0718 

o764 

0810 

6 

53 

7078 

7I24 

7i69 

72l5 

7260 

73o6 

6 

54 

o857 

o9o3 

0949 

o995 

io4i 

io87 

5 

54 

735i 

7397 

7442 

7488 

7533 

7579 

5 

.  55 

1  1  34 

1180 

1226 

I272 

i3i8 

1  364 

4 

55 

7624 

767o 

77i5 

776i 

7806 

785i 

4 

56 

i4io 

i457 

i5o3 

I  549 

i595 

i64i 

3 

56 

7897 

7942 

7988 

8o33 

8o79 

8124 

3 

57 

1687 

i733 

1780 

:826 

l872 

1918 

2 

57 

8170 

82i5 

8261 

83o6 

835i 

8397 

2 

58 

i964 

2010 

2o56 

2IO2 

2l49 

2195 

I 

58 

8442 

8488 

8533 

8579 

8624 

8669 

1 

59 

224l 

2287 

2333 

2379 

2425 

2471 

O 

59 

87i5 

8760 

8806 

885i 

8897 

8942 

O 

60" 

50" 

40" 

30" 

20" 

10" 

a 

60" 

50"  |  40" 

?0" 

20" 

10" 

. 

Co-tangent  of  57  Degrees. 

a 

Co-tangent  of  56  Degrees. 

a 

f  1  //  a//  o//  AH  c//  en  7/7  Q//  a/i 
P  T*nrt  I  •*•*•**    ^*    **    "D    '    o    I/ 

.  (  1"  2"  3"  4"  5"  6"  7"  8"  9" 

ir  I  5   9  14  18  23  27  32  37  41 

58 


LOGARITHMIC    SINES 


.3 

Sine  of  34  Degrees. 

rf 

Sine  of  35  Degrees. 

1 

s 

0" 

10" 

20"   30" 

40" 

50" 

s 

0"    |  10"  |  20" 

30'' 

40" 

50" 

o 

9.747562 

7593 

7624  7655 

7686 

7718 

59 

o  9.75859i  8621 

865i 

8681  8712 

8742 

59 

I 

7749 

778o 

7811  7842 

7874 

79°5 

58 

i 

87728802 

8832  8862i8892 

8922 

58 

2 

7936 

7967 

7998  8o3o 

8061 

8o92 

57 

2 

8952  8982 

9OI2|9042  9072 

9IO2 

57 

L 

8i23 
83io 

8i54 
834i 

8i8582i6 
8372  84o3 

8248 
8434 

8466 

56 
55 

L 

9l32  9l62 
93l2  9342 

9192  9222  9262 

9372  94o2  9432 

9282 
9462 

56 
55 

5 

8497 

8528  85598590 

8621 

8652 

54 

5 

9492  9522 

95529582 

9612 

9642 

54 

6 

8683 

87i4 

8745,8777 

8808 

8839 

53 

6 

9672 

9702 

9732 

9762 

9792 

9822 

53 

7 

8870 

8901 

89328963 

8994 

9025 

52 

7 

9852 

988i 

99" 

994i 

99-71 

...  I 

52 

8 

9o56 

9o87 

9118  9149 

9180 

92I2 

5i 

8 

9.  76003  1 

0061 

0091 

OI2I 

oi5i 

0181 

5i 

9 

9243 

9274'93o59336 

9367 

9398 

5o 

9 

O2I  I 

0240 

0270 

o3oo 

o33o 

o36o 

5o 

10 

9.749429 

9460  9491  9522 

9553 

9584 

49 

IO 

9.  760390 

0420 

o45o 

o48o 

0509 

o539 

49 

n 

96i5 

9646  967-7  9-708 

9739 

9770 

48 

n 

o569 

o599 

0629 

o659 

0689 

0718 

48 

12 

98oi 

9832 

9863  9894 

9925 

9956 

47 

12 

o748 

o778 

0808 

o838 

0868 

0898 

47 

i3 

9987 

..18 

..48..  79 

.  no 

46 

\l 

0927 

o957 

o987 

IOI7 

io47 

1076 

46 

i4 

9.  750172 

0203 

0234  0265 

O296 

0327 

45 

i4 

I  I  06 

ii36 

1166 

1196 

1225 

1255 

45 

i5 

o358 

0389 

0420  o45i 

0482 

O5l2 

44 

i5 

1285 

i3i5 

1  345 

i374 

i4o4 

i434 

44 

16 

o543 

o574  o6o5;o636 

066-7 

o698 

43 

16 

1  464 

i494 

i523 

i553 

i583 

i6i3 

43 

I7 

o729 

0760 

0791 

0821 

o852 

o883 

42 

17 

1642 

16-72 

I702 

I732 

i76i 

1791 

42 

18 

o9M 

0945  O976  ioo7 

io37 

1068 

4i 

18 

1821 

i85i 

1880 

1910 

1940 

1969 

4i 

19 

io99 

ii3o 

i  i6i|i  192 

1222 

1253 

4o 

'9 

1999 

2O29 

2059 

2088 

21  18 

2148 

4o 

20 

9.75i284 

i3i5 

i346  1377 

i4o7 

i438 

39 

20 

9.762i77 

22O7 

2237 

2267 

2296 

2326 

39 

21 

i469 

i5oo 

i53i 

i56i 

l592 

1623 

38 

21 

2356 

2385 

24i5 

2445 

2474 

25o4 

38 

22 

i654 

1  685 

1715  1746 

I777 

1808 

37 

22 

2534 

2563 

2593 

2623 

2652 

2682 

37 

23 

i839 

1869 

1900  1931 

I962 

I992 

36 

23 

27I2 

274i 

277I 

2801 

283o 

2860 

36 

24 

2O23 

2o54  2o85  2ii5 

2146 

2I77 

35 

24 

2889 

29I9 

2949 

2978 

3oo8 

3o38 

35 

25 

22O8 

2238 

2269  23oo 

233o 

236i 

34 

25 

3o67 

3o97 

3i26 

3i56 

3i86 

32i5 

34 

26 

2392 

3423,2453  2484 

25i5 

2545 

33 

26 

3245 

3274 

33o4 

3333 

3363 

3393 

33 

27 

2576 

26o7  2637 

2668 

2699 

2729 

32 

27 

3422 

3452 

348i 

35ii 

354o 

357o 

32 

28 

2760 

279I 

2822  2852 

2883 

29i4 

3i 

28 

36oo 

3629 

3659 

3688 

37i8 

3747 

3i 

29 

2944 

2975 

3oo5  3o36 

3o67 

3o97 

3o 

29 

3777 

38o6 

3836 

3865 

3895 

3925 

3o 

3o 

9.753i28 

3i59 

3l8g  3220 

325i 

3281 

29 

3o 

9.763954 

3984 

4oi3 

4o43 

4o72 

4102 

29 

3i 

33i2 

3342 

3373  34o4 

3434 

3465 

28 

3i 

4i3i 

4i6i 

4i9o 

4249 

4279 

28 

32 

.   3495 

3526  3557 

3587 

36i8 

3648 

27 

32 

43o8 

4338 

4367 

4396 

4426 

4455 

27 

33 

3679 

37io  374o 

377i 

38oi 

3832 

26 

33 

4485 

45i4 

4544 

4573 

46o3 

4632 

26 

34 

3862 

3893 

3923 

3954 

3985 

4oi5 

25 

34 

4662 

469i 

4720 

475o 

4779 

48o9 

25 

35 
36 

4o46 

4229 

4o76  4io7 
42594290 

4i37 

4320 

4i684i98 
435i  438i 

24 
23 

35 
36 

4838 
5oi5 

4868 
5o44 

4897 
5o74 

5io3 

4g56 

4985 
5i62 

24 
23 

37 

44  1  2 

4442 

4473 

45o3 

4534  4564 

22 

37 

5i9i 

5221 

525o 

5279 

53o9 

5338 

22 

38 

4595 

46254656 

4686 

47i74747 

21 

38 

5367 

5397 

5426 

5456 

5485 

55i4 

21 

39 

4778 

48o8  4839 

4869 

49oo  493o 

20 

39 

5544 

5573 

56o2 

5632 

566i 

5690 

20 

4o 

9.  754960 

4991  5o2t 

5o52 

5o82:5n3 

I9 

4o 

9.  765720 

5749 

5778 

58o8 

5837 

5866 

I9 

4i 

5i43 

5i73 

52o4 

5234 

5265  5295 

18 

4i 

5896 

5925 

5954 

5984 

6oi3 

6042 

18 

42 

5326 

53565386 

54i7 

54475478 

17 

42 

6072 

6101 

6i3o 

6i59 

6189 

6218 

i7 

43 

55o8 

5538 

5569 

5599 

5629566o 

16 

43 

6247 

6277 

63o6 

6335 

6364 

6394 

16 

44 

5690 

572I 

575i 

578i 

58i2;5842 

i5 

44 

6423 

6452 

648  1 

65n 

654« 

6569 

i5 

45 

5872 

59o3 

5933 

5963 

5994  6024 

i4 

45 

6598 

6628 

6657 

6686 

67i5 

6745 

i4 

46 

6o54 

6o856n5 

6i45 

61766206 

i3 

46 

6774 

68o3 

6832 

6862 

6891 

6920 

i3 

47 

6236 

6267  6297 

6327 

63586388 

12 

47 

6949 

6978 

7oo8 

7°37 

7o66 

7o95 

12 

00  O  O 
xjxjvo 

64i8 
6600 
9.756782 

6448  6479 
663o  6660 
6812  6842 

65o96539|657o 
669ii672i:675i 
6872  69o3  6933 

IO 

9 

48 

49 
5o 

7124 
73oo 

9.  767475 

7i54 
7329 
75o4 

7i83 
7358 
7533 

7212 
7387 
7562 

•7241 
74i6 
759i 

•7270 
7445 

7620 

I  I 
IO 

9 

5i 

6963 

6993  7O23 

7o54 

708417114 

8 

5i 

7679 

77o8 

7737 

7766 

7795 

8 

52 

7i44 

7i75  72o5 

7235 

7265  7295 

7 

52 

7824 

7853 

•7882 

-7912 

794i 

797° 

7 

53 

7326 

7356  7386 

74i6 

7446  7477 

6 

53 

7999 

8028 

8o57 

8086 

3ii5 

8i44 

6 

54 

7507 

7537  7567 

7597 

7627  7658 

5 

54 

8i73 

82o3 

8232 

8261 

^290 

83i9 

5 

55 

7688 

77187748 

7778 

7808  7839 

4 

55 

83488377 

84o6  8435 

8464 

8493  4 

56 

7869 

7899  7929  7959 

7989  8oi9 

3 

56 

85228551 

8580860986388668 

3 

57 
58 

8o5o 
823o 

8080  8110  8i4o 
826082908321 

8170  8200 
835i  838i 

2 

57 
58 

8697  8726 
8871  89oo 

87558784 
8929!8958 

88  1  3  8842 
8987  9016 

2 

59 

84ii 

844i  8471  85oi 

853i  856i 

O 

59 

9o45  9o74  9io3  9i32  9i6i 

9i9o 

O 

60" 

50"  : 

40"   30"   20"   10" 

. 

60"     50"   40"  |  30"   20" 

10"  1 

Co-sine  of  55  Degrees. 

s 

Co-sine  of  54  Degrees. 

§ 

P'*H13  2e'  39" 

4"  5"  6"  7"  8"  9" 
12  15  18  21  25  28 

p  p  .<  1"  2"  3"  4"  5"  6"  7"  B"  9" 
}  3   6   9  12  15  18  21  24  27 

LOGARITHMIC    TANGENTS. 


1  — 

-S 

Tangent  of  34  Degrees. 

.3 

Tangent  of  35  Degrees. 

9 

0" 

10"  |  20" 

30" 

40"   50" 

9 

0" 

10" 

20" 

30" 

40" 

50" 

0 

9.828987 

9o339o78 

9124 

9i6g!92i5 

59 

o 

9.  845227 

5272 

53i6 

536i 

54o6 

545  1 

59 

I 

9260 

93o5935i 

9396 

9442 

9487  58 

I 

5496 

554o 

5585 

563o 

5675 

572O 

58 

2 

9532 

9578 

9623 

9669 

97i4 

9759 

57 

2 

5764 

58o9 

5854 

5899 

5944 

5988 

57 

0 

9805 

985o 

9895  gg4i 

9986 

..32 

56 

3 

6o33 

6o78 

6i23 

6168 

6212 

6257 

56 

4 

9.830077 

0122 

0!68 

02l3 

0258 

o3o4 

55 

4 

63o2 

6347 

639i 

6436 

648i 

6526 

55 

c 

o349 

o395 

o44o 

o485 

o53i 

o576 

54 

5 

6570 

66i5 

6660 

67o5 

675o 

6794 

54 

6 

0621 

o667 

07I2 

°757 

o8o3 

0848 

53 

6 

6839 

6884 

6929 

6973 

7oi8 

7o63 

53 

7 

0893 

o939 

o984 

1029 

io75 

1120 

52 

7 

7108 

7i52 

7i97 

-7242 

7287 

733i 

52 

n65 

I2II 

1256 

i3oi 

i347 

i392 

5! 

8 

7376 

742i 

7465 

75io 

7555 

76oo 

5i 

9 

i437 

i483 

i528 

i573 

i6i9 

1  664 

5o 

9 

7644 

7689 

7734 

7779 

7823 

-7868 

5o 

10 

9.831709 

i755 

1800 

i845 

i89i 

i936 

49 

IO 

9.8479i3 

7957 

8002 

8047 

8092 

8i36 

49 

ii 

1981 

2026 

2O72 

2117 

2162 

2208 

48 

ii 

8181 

8226 

8270 

83i5 

836o 

84o5 

48 

12 

2253 

2298 

2343 

2389 

2434 

2479 

4? 

12 

8449 

8494 

8539 

8583 

8628 

8673 

47 

i3 

2525 

257O 

26i5 

2660 

2-706 

2751 

46 

i3 

87i7 

8762 

8807 

885i 

8896 

894i 

46 

i4 

2796 

2842 

2887 

2932 

2977 

3o23 

45 

i4 

8986 

9o3o 

9o75 

9I20 

9164 

9209 

45 

i5 

3o68  3n3 

3i58 

3204 

3249 

3294 

44 

i5 

9254 

9298 

9343 

9388 

9432 

9477 

44 

16 

3339 

3385 

343o 

3475 

3520 

3566 

43 

16 

9522 

9566 

96n 

9656 

97oo 

9745 

43 

!7 

36ii 

3656 

37oi 

3747 

3792 

3837 

42 

17 

979° 

9834 

9879 

9924 

9968 

.  .i3 

42 

'  18 

3882 

3927 

3973 

4oi8 

4o63 

4io8 

4i 

18 

9.85oo57 

OIO2 

0147 

oi9i 

0236 

0281 

4i 

19 

4i54 

4199 

4244 

428g 

4334 

438o 

4o 

i9 

o325 

0370 

o4i5 

o459 

o5o4 

o548 

4o 

20 

9.834425 

447o 

45:5 

456i 

46o6 

465i 

39 

20 

9.85o593 

o638 

0682 

0727 

°772 

0816 

39 

21 

4696 

474i 

4787 

4832 

4877 

4922 

38 

21 

0861 

o9o5 

o95o 

o995 

1039 

1084 

38 

22 

4967 

5012 

5o58 

5io3 

5i48 

5i93 

37 

22 

II29 

u73 

1218 

1262 

i3o7 

i352 

37 

23 

5238 

5284 

5329 

5374 

54i9 

5464 

36 

23 

i396 

i44i 

i485 

i53o 

i575 

i6i9 

36 

24 

55o9 

5555 

56oo 

5645 

569o 

5735 

35 

24 

1  664 

1708 

i753 

i797 

1842 

i887 

35 

25 

5780 

5826 

587i 

59i6 

596i 

5oo6 

34 

25 

I93i 

i976 

2O2O 

2o65 

2110 

2i54 

34 

26 

6o5i 

6o96 

6  1  42 

6i87 

6232 

6277 

33 

26 

2199 

2243 

2288 

2332 

2377 

2422 

33 

27 

6322 

6367 

6412 

6458 

65o3 

6548 

32 

27 

2466 

25ll 

2555 

2600 

2644 

2689 

32 

28 

6593 

6638 

6683 

6728 

6773 

68i9 

3i 

28 

2733 

2778 

2823 

286-7 

2912 

2956 

3i 

29 

6864 

69o9 

6954 

6999 

7o44 

7o89 

3o 

29 

3ooi 

3o45 

3ogo 

3i34 

3i79 

3223 

3o 

3o 

9.837i34 

7J79 

7225 

7270 

73i5 

736o 

29 

3o 

9.  353268 

33i3 

3357 

3402 

3446 

349i 

29 

3i 

74o5 

745o 

7495 

754o 

7585 

763o 

28 

3i 

3535 

358o 

3624 

3669 

37i3 

3758 

28 

32 

7675 

7721 

7766 

78n 

7856 

79oi 

27 

32 

38o2 

3847 

38gi 

3936 

398o 

4o25 

27 

33 

7946 

7991 

8o36 

8081 

8126 

8171 

26 

33 

4o69 

4n4 

4i58 

4203 

4247 

4292 

26 

34 

8216 

8261 

83o7 

8352 

8397 

8442 

25 

34 

4336 

438i 

4425 

447o 

45i4 

4559 

25 

35 

8487 

8532 

86778622 

8667 

8712 

24 

35 

46o3 

4648 

4692 

4737 

4781 

4826 

24 

36 

8757 

8802 

8847 

8892 

8937 

898a 

23 

36 

487o 

49i5 

4959 

5oo4 

5o48 

5o93 

23 

37 

9027 

9072 

9n7 

9l62 

9207 

9252 

22 

37 

5i37 

5i82 

5226 

527I 

53i5 

536o 

22 

38 

9297 

9343 

9388 

9433 

9478 

9523 

21 

38 

54o4 

5449 

5493 

5537 

5582 

5626 

21 

39 

9568 

96i3 

9658 

97o3 

9748 

9793 

2O 

39 

567i 

57i5 

5760 

58o4 

5849 

5893 

2O 

4o 

9.839838 

9883 

9928 

9973 

..18 

..63 

I9 

4o 

9.855938 

5982 

6026 

6071 

6n5 

6160 

19 

4i 

9.84oio8 

oi53 

oi98 

0243 

0288 

o333 

18 

4i 

6204 

6249 

6293 

6338 

6382 

6426 

1  8 

42 

o378 

0423 

o468 

o5i3 

o558 

o6o3 

'7 

42 

647i 

65i5 

656o 

66o4 

6649 

66g3 

17 

43 

o648 

o693 

o737 

0-782 

0827 

0872 

16 

43 

6737 

6782 

6826 

6871 

6915 

6959 

16 

44 

o9i7 

0962 

100-7 

1052 

io97 

Il42 

i5 

44 

7oo4 

7o48 

7o93 

7i37 

-7182 

7226 

i5 

45 

n87 

1232 

I277 

1322 

i367 

l4l2 

i4 

45 

7270 

73i5 

7359 

7404 

7448 

7492 

i4 

46 

i457 

1502 

1  54? 

l592 

i637 

1682 

i3 

46 

7537 

758i 

7626 

7670 

77i4 

775g 

i3 

47 

I727 

1771 

1816 

1861 

1906 

i95i 

12 

47 

78o3 

7848 

7892 

7936 

7981 

8c25 

12 

48 

I996 

2o4l 

2086 

2l3l 

2176 

2221 

I  I 

48 

8o69 

8n4 

8i58 

8203 

8247 

829i 

II 

49 

2266 

23ll 

2355 

2400 

2445 

2490 

IO 

49 

8336 

838o 

8424 

8469 

85i3 

8558 

10 

5o 

9  842535 

2  5  80 

2625 

26-70 

2715 

2760 

9 

5o 

9.  858602 

8646 

869i 

8735 

8779 

8824 

9 

5i 

28o5 

2849 

2894 

2939 

2984 

3o29 

8 

5i 

8868 

89I2 

8957 

9ooi 

9045 

9090 

8 

52 

3o74 

3ii9 

3i64 

3209 

3253 

3298 

7 

52 

9i34 

9i78 

9223 

9267 

93n 

9356 

7 

53 

3343 

3388 

3433 

3478 

3523 

3568 

6 

53 

94oo 

9444 

9489 

9533 

9577 

9622 

6 

54 

36i2 

3657 

3702 

3747 

3792 

3837 

5 

54 

9666 

97io 

9755 

9799 

9843  9888 

5 

55 

3882 

3927 

397i 

4oi6 

4o6i 

4io6 

4 

55 

9932 

9976 

.  .21 

..65 

.109).  i54 

4 

56 

4i5i 

4i96 

4241 

4285 

433o 

4375 

3 

56 

9.86oi98 

0242 

0287 

o33i 

o375io42o 

3 

57 

4420 

4465 

45io 

4554 

45gg 

4644 

2 

57 

o464 

o5o8 

o552 

o597  o64i  o685 

2 

58 
59 

4689 
4958 

4734 
5oo3 

4779 
5o48 

4823 
5o92 

4868 
5i37 

5?82 

I 
0 

58 
59 

o73o 
o995 

0774 
io4o 

0818 
io84 

0862  090-7,0951 

II28JII72  1217 

I 
O 

60" 

50"   40" 

30" 

20" 

10" 

. 

60"    [  50"   40"   30"   20"  j  10" 

a 

Co-tangent  of  55  Degrees. 

& 

Co-tangent  of  54  Degrees. 

.<  \"  2"  3"  4"  5"  6"  7"  8"  9" 

.(  1"  2"  3"  4"  5"  6"  7"  S"  9" 

in\  5   9  14  18  23  27  32  36  41 

irtl  4  9  13  18  22  27  31  36  40 

LOGARITHMIC    SINES. 


d 
D 

Sine  of  36  Degrees. 

_s- 

Sine  of  37  Degrees. 

H 

0" 

10"   20" 

30' 

40"   50" 

s 

0" 

10" 

20"  |  30"  1  40" 

50" 

o 

9.769219 

92489277 

93o6 

93359364i59 

o 

9-779463 

949i 

95i9|9547  9575 

9603 

59 

i 

9393 

9421 

945o  9479 

95o8  953-7 

58 

i 

963i 

9659 

9686  97i4  9742 

977° 

58 

2 

9566 

9595 

96249653 

9682  9711 

5? 

2 

9798 

9826 

9854 

9882 

9910 

9938 

57 

3 

974o 

9769 

97989827 

9856  9884 

56 

3 

9966 

9993 

.  .21 

.  .49 

••77 

.io5 

56 

4 

99i3 

9942 

997i 

.  .  .  . 

..29 

..58 

55 

4 

9.  78oi33 

0161 

oi89 

0216 

0244 

0272 

55 

5 

9.770087 

0116 

oi45  0173 

O202  O23l 

54 

5 

o3oo 

o328 

o356 

o384 

o4n 

o439 

54 

6 

0260 

0289 

o3i8o347 

0376  o4o4 

53 

6 

0467 

o495 

o523 

o55i 

o578 

0606 

53 

7 

o433 

0462 

o49i 

O520 

o549jo577 

52 

7 

o634 

0662 

o69o 

0718 

o745 

077$ 

52 

8 

0606 

o635 

o664  o693 

072210750 

5i 

8 

0801 

o829 

o857 

0884 

0912 

0940 

5i 

9 

0779 

0808 

08370866 

0895  0923 

5o 

9 

o968 

o996 

1023 

io5i 

1079 

1107 

5o 

10 

9.7709520981 

IOIO 

io39 

1067  1096 

49 

IO 

9.781134 

1162 

II9O 

1218 

1246 

1273 

49 

ii 

ii25ii54 

n83 

121  I 

1240)1269 

48 

ii 

i3oi 

i329 

i357 

1  384 

l4l2 

i44o 

48 

12 

1298  i326 

i355 

1  384 

i4i3  i44i 

47 

12 

i468 

i495 

i523 

i55i 

1578 

1606 

47 

i3 

1470 

1499 

i528 

i556 

i585  1614 

46 

i3 

i634 

1662 

i689 

1717 

1745 

1772 

46 

i4 

1  643 

1671 

1700 

I729 

1758  1786 

45 

i4 

1800 

1828 

i856 

i883 

1911 

1939 

45 

i5 

i8i5 

1  844 

1872 

I9OI 

i93oi959 

44 

i5 

i966 

i994 

2O22 

2049 

2077 

2105 

44 

16 

1987 

2016 

2o45 

2073 

2102  2l3l 

43 

16 

'    2l32 

2160 

2188 

22l5 

2243 

2271 

43 

17 

2159 

2188 

2217 

2245 

2274  23o3 

42 

17 

2298 

2326 

2354 

238i 

2409 

2437 

42 

18 

233i 

236o 

2389 

2417 

2446  2475 

4i 

18 

2464 

2492 

252O 

2547 

2575 

2602 

4i 

I9 

25o3 

2532 

256i 

2589 

2618  2646 

4o 

i9 

263o 

2658 

2685 

2713 

2741 

2768 

4o 

20  9.  772675 

2704 

2732 

2761 

2790 

2818 

39 

20 

9.782796 

2823 

285i 

2879 

2906 

2934 

39 

21 

2847 

2875 

2904 

2933 

2961 

2990 

38 

21 

296i 

2989 

3017 

3o44 

3072 

3o99 

38 

22 

3oi8 

3o47 

8076 

3io4 

3i33 

3i6i 

37 

22 

3127 

3i54 

3i82 

3210 

3237 

3265 

37 

23 

3190 

3219 

3247 

3276 

33o4 

3333 

36 

23 

3292 

3320 

3347 

3375 

34o2 

343o 

36 

24 

336i 

3390 

34i8 

3447 

3476 

35o4 

35 

24 

3458 

3485 

35i3 

354o 

3568 

3595 

35 

25 

3533 

356i 

359o 

36i8 

3647 

3675 

34 

25 

3623 

365o 

3678 

37o5 

3733 

376o 

34 

26 

3704 

3732 

376i 

3789 

38i8 

3846 

33 

26 

3788 

38i5 

3843 

3870 

3898 

3925 

33 

27 

3875 

3903 

396o 

3989 

4017 

32 

27 

3953 

39«o  4oo8 

4o35 

4o63 

4o9o 

32 

28 

4o46 

4074 

4io34i3i 

4i6o 

4i88 

3i 

28 

4n8 

4i45 

4i73 

4200 

4228 

4255 

3i 

29 

4217 

4245 

4274 

4302 

433i 

4359 

3o 

29 

4282 

43io 

4337 

4365 

4392 

4420 

3o 

309.774388 

44x6 

4445  4473 

45oi 

453o 

29 

3o 

9  .  784447 

4475 

45o2 

4529 

4557 

4584 

29 

3i 

4558 

4587 

46i546444672 

4700 

28 

3i 

4612 

4639 

4667 

4594 

4721 

4749 

28 

32 

4729 

4757 

4786  48i4'4842 

487i 

27 

32 

4776 

48o4 

483i 

4858 

4886 

49i3 

27 

33 
34 

4899 
5070 

4928 
5098 

495649855oi3|5o4i 
5i265i55|5i8352i2 

26 

25 

33 

34 

494i 
5io5 

4968 
5i32 

4995 
5  1  60 

5o23 
5187 

5o5o 
52i4 

5o78 
5242 

26 
25 

35 

524o 

5268 

5297 

53255353 

5382 

24 

35 

5269 

5296 

5324 

535i 

5378 

54o6 

24 

36 

54io 

5438 

5467  5495 

5523 

5552 

23 

36 

5433 

546i 

5488 

55i5 

5543 

557o 

23 

37 

558o 

56o8 

56375665 

5693 

5722 

22 

37 

5597 

5624 

5652 

5679 

57o6 

5734 

22 

38 

575o 

5778 

58o7 

5835  5863 

5892 

21 

38 

576i 

5788 

58i6 

5843 

587o 

5898 

21 

39 

5920 

5948 

5977 

6oo5 

6o33 

6061 

2O 

39 

5925 

5952 

5979 

6007 

6o34 

6061 

2O 

4o'9«  776090 

61186146 

61756203 

623i 

'9 

4o 

9.786o89 

6116 

6i43 

6170 

6198 

6225 

I9 

4i 

6259 

6288  63i6 

63446372 

64oi 

18 

41 

6252 

6279 

63o7 

6334 

636i 

6388 

18 

42 

6429 

6457 

6485 

65i46542 

657o 

17 

42 

64i6 

6443 

647o 

6497 

6525 

6552 

'7 

43 
44 

6598 
6768 

6627 
6796 

6655 
6824 

6683 
6852 

6711 
6880 

6739 
69o9 

16 
i5 

43 
44 

6579 
6742 

6606  6634 
6770  6707 

6661 
6824 

6688 
685i 

67i5 

6878 

16 
i5 

45 

6937 

6965 

6993 

7021 

7o5o 

7078 

i4 

45 

69o6 

6933 

696o 

6987 

7014 

7042 

i4 

46 

7106 

7i34 

7162 

7191 

7219 

7247 

i3 

46 

7o69 

7096 

7123 

7i5o 

7177 

72o5 

!3 

47 

7275 

73o3 

733i 

7359 

7388 

74i6 

12 

47 

7232 

7259 

7286 

73i3 

734o 

7367 

12 

48 

7444 

7472 

75oo 

7528 

7556 

7585 

II 

48 

7395 

7422 

7449 

7476  75o3 

753o 

II 

49 

7613 

764i 

7669 

7697 

7725 

7753 

IO 

49 

7557 

7585 

7612 

7639  7666 

7693 

10 

5o 
5i 

9.777781 
795o 

7810 
7978 

7838 
8006 

7866  7894 
80348062 

7922 

8o9i 

| 

5o 
5i 

o.  787720 
7883 

7747 
79io 

7774 
7937 

7801 
7964 

7829 
799  l 

7856 
8018 

1 

52 

8119 

8i4? 

8175 

8203 

823i 

8259 

7 

52 

8o45 

8072 

8o99 

8127 

8i54 

8181 

7 

53 

8287 

83i5 

8343 

837i 

8399 

8427 

6 

53 

8208 

8235 

8262 

8289 

83i6 

8343 

6 

54 

8455 

8483 

85n 

85398567 

8595 

5 

54 

837o 

8397 

8424 

845  1 

8478 

85o5 

5 

55 

8624 

8652 

8680 

870818736 

8764 

4 

55 

8532 

8559 

8586 

86i3 

864o 

8667 

4 

56 

8792 

8820 

8848 

8876180.04 

8932 

3 

56 

86^8721  8748 

8775 

8802 

8829 

3 

57 

8960 

8988 

9oi6 

9o44 

9072 

9ioo 

2 

57 

8856  8883  89io 

89378964899i 

2 

58 

9128 

9i56 

9i83 

92II 

9239 

9267 

I 

58 

9oi8  9o45  9072 

9099  9126  91  53 

I 

59 

9295 

9323 

935i 

93799407 

9435 

0 

59 

9i8o  92O7'9234!926i  9288  93i5  o 

60" 

50" 

40" 

30"   20" 

10" 

d 

60"     50"   40"  i  30"   20"   10" 

Co-sinb  of  53 

Degrees. 

§ 

Co-sine  of  52  Degrees.     % 

P  Parti  l"  2//  3"  4" 

5"  6"  7"  8"  9" 

p  p  A  \"  2"  3"  4"  5"  6"  7"  8"  9" 

l.rartj  3   6   9  n 

14  17  20  23  26 

m\  *   5   8  11  14  16  19  22  25 

LOGARITHMIC    TANGENTS. 


.s 

Tangent  of  36  Degrees. 

£ 

Tangent  of  37  Degrees. 

m 

0" 

10" 

20" 

30" 

40" 

50" 

s 

0" 

10" 

20" 

30" 

40" 

50" 

0 

9.861261 

i3o5 

i35o 

i394 

i438 

1482 

59 

O 

9-877114 

7i58 

7202 

7246 

7290 

7333 

59 

1 

1527 

1571 

1616 

:659 

1704 

1748 

58 

I 

7377 

742I 

7465 

75o9 

7552 

7596 

58 

2 

1792 

1837 

1881 

I925 

i969 

2Ol4 

57 

2 

7640 

7684 

7?28 

777i 

78i5 

7859 

57 

3 

2o58 

2102 

2!46 

2  I  01 

2235 

2279 

56 

3 

79°3 

7947 

799° 

8o34 

8078 

8122 

56 

4 

2323 

2368 

2412 

s456 

25oo 

2545 

55 

4 

8i65 

8209 

8253 

8297 

834i 

8384 

55 

5 

2689 

2633 

2677 

2721 

2766 

2810 

54 

5 

8428 

8472 

85i6 

8559 

86o3 

8647 

54 

6 

2854 

2898 

2943 

2987 

3o3i 

3075 

53 

6 

869i 

8734 

8778 

8822 

8866 

89o9 

53 

7 

3119 

3i64 

3208 

3252 

3296 

334i 

52 

7 

8953 

8997 

9041 

9o85 

9128 

9I72 

52 

8 

3385 

3429 

3473 

35i7 

3562 

36o6 

5i 

8 

9216 

9260 

93o3 

9347 

939i 

9435 

5i 

9 

365o 

3694 

3738 

3783 

3827 

3871 

5o 

9 

9478 

9522 

9566 

96o9 

9653 

9697 

5o 

10 

9.8639i5 

3959 

4oo4 

4o48 

4092 

4i36 

49 

10 

9-879741 

9784 

9828 

9872 

99i6 

9959 

49 

ii 

4i8o 

4225 

4269 

43i3 

4357 

44oi 

48 

ii 

9.88ooo3 

0047 

0091 

oi34 

0178 

O222 

48 

12 

4445 

449o 

4534 

4578 

4622 

4666 

47 

12 

0265 

oSog 

o353 

o397 

o44o 

o484 

47 

i3 

4710 

4755 

4799 

4843 

4887 

493i 

46 

i3 

o528 

o57i 

o6i5 

o659 

0703 

o746 

46 

i4 

4975 

5O2O 

5o64 

5io8 

5i52 

5i96 

45 

i4 

079o 

o834 

o877 

092I 

o965 

1008 

45 

i5 

5240 

5285 

5329 

5373 

54i7 

546i 

44 

i5 

IO52 

1096 

n4o 

n83 

1227 

1271 

44 

16 

55o5 

5549 

5594 

5638 

5682 

5726 

43 

16 

i3i4 

i358 

1402 

i445 

i489 

i533 

43 

|7 

5770 

58i4 

5858 

5'9o3 

5947 

599i 

42 

17 

i577 

1620 

1  664 

I7o8 

1751 

i795 

42 

18 

6o35 

6o79 

6i23 

6167 

6211 

6256 

4i 

18 

i839 

1882 

1926 

I97° 

20l3 

2067 

4i 

J9 

63oo 

6344 

6388 

6432 

6476 

6520 

4o 

J9 

aioi 

2i44 

2188 

2232 

2275 

23i9 

4o 

20 

9.866564 

66o9 

6653 

6697 

6741 

6785 

39 

20 

9.  882363 

2406 

245o 

2494 

2537 

258i 

39 

21 

6829 

6873 

6917 

696i 

7006 

7o5o 

38 

21 

2625 

2668 

27I2 

2756 

2799 

2843 

38 

22 

7094 

7i38 

7182 

7226 

7270 

73i4 

37 

22 

2887 

2930 

2974 

3oi8 

3o6i 

3io5 

37 

23 

7358 

7402 

7446 

749i 

7535 

7579 

36 

23 

3i48 

3192 

3236 

32-79 

3323 

3367 

36 

24 

7623 

7667 

7711 

7755 

7799 

7843 

35 

24 

34io 

3454 

3498 

354i 

3585 

3628 

35 

25 

7887 

793i 

7975 

8oi9 

8o64 

8108 

34 

25 

3672 

37i6 

3759 

38o3 

3847 

389o 

34 

26 

8i52 

8i96 

8240 

8284 

8328 

8372 

33 

26 

3934 

3977 

4O2I 

4o65 

4io8 

4i52 

33 

27 

84i6 

846o 

85o4 

8548 

8592 

8636 

32 

27 

4i96 

4239 

4283 

4326 

437o 

44i4 

32 

28 

8680 

8724 

8768 

88i3 

8857 

89oi 

3i 

28 

4457 

45oi 

4544 

4588 

4632 

4675 

3i 

29 

8945 

8989 

9o33 

9°77 

9I2I 

9i65 

3o 

29 

4719 

4-762 

48o6 

485o 

4893 

4937 

3o 

3o 

0.860209 

9253 

9297 

934i 

9385 

9429 

29 

3o 

9.88498o 

5o24 

5o68 

5m 

5i55 

5i98 

29 

3i 

9473 

95l7 

956i 

96o5 

9649 

9693 

28 

3i 

5242 

5286 

5329 

5373 

54i6 

546o 

28 

32 

9?3? 

9781 

9825 

9869 

99i3 

9957 

27 

32 

55o4 

5547 

559i 

5634 

5678 

5721 

27 

33 

9.870001 

oo45 

oo89 

oi33 

0177 

O22I 

26 

33 

5765 

58o9 

5852 

5896 

5939 

5983 

26 

34 

O265 

oSog 

o353 

o397 

o44i 

o485 

25 

34 

6026 

6o7o 

6n4 

6i57 

6201 

6244 

25 

35 

0529 

o573 

0617 

0661 

0705 

0749 

24 

35 

6288 

633i 

6375 

64i9 

6462 

65o6 

24 

36 

o793 

6837 

0881 

6925 

o969 

ioi3 

23 

36 

6549 

6593 

6636 

6680 

6723 

6767 

23 

3? 

1057 

IIOI 

n45 

u89 

1233 

1277 

22 

37 

•  6811 

6854 

6898 

694i 

6985 

7028 

22 

38 

1321 

i365 

i4o9 

i453 

i497 

i54i 

21 

38 

7072 

7116 

7i59 

72O2 

7246 

7289 

21 

39 

i585 

1629 

i673 

1717 

1761 

i8o5 

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39 

7333 

7377 

7420 

7464 

75°7 

755i 

2O 

4o 

9.871849 

1893 

i937 

i98o 

2024 

2068 

1  9 

4o 

9.887594 

7638 

768i 

7725 

7768 

7812 

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4i 

2112 

2i56 

230O 

2244 

2288 

2332 

18 

4i 

7855 

7899 

7942 

7986 

8o29 

8o73 

18 

42 

2376 

2420 

2464 

25o8 

2552 

2596 

17 

42 

8116 

8160 

8203 

8247 

829I 

8334 

17 

43 

264o 

2684 

2727 

2771 

2815 

2859 

16 

43 

8378 

8421 

8465 

85o8 

8552 

8595 

16 

44 

29O3 

2947 

299I 

3o35 

3079 

3i23 

i5 

44 

8639 

8682 

8-726 

8769 

88i3 

8856 

16 

45 

3i67 

3211 

3255 

3299 

3342 

3386 

i4 

45 

89oo 

8943 

8987 

9o3o 

9Q74 

9117 

i4 

46 

343o 

3474 

35i8 

3562 

36o6 

365o 

i3 

46 

9161 

9204 

9248 

9291 

9334 

9378 

i3 

4? 

3694 

3738 

3781 

3825 

3869 

39i3 

12 

47 

9421 

9465 

95o8 

9552 

9595 

9639 

12 

48 

3957 

4ooi 

4o45 

4o89 

4i33 

4177 

II 

48 

9682 

9726 

9769 

9813 

9856 

9900 

II 

49 

4220 

4264 

43o8 

4352 

4396 

444o 

10 

49 

9943 

9987 

..3o 

..74 

.117 

.160 

10 

5o 

9,874484 

4528 

4572 

46i5 

4659 

47o3 

9 

5o 

9.890204 

0247 

029I 

o334 

0378 

O42I 

9 

5i 

4747 

4791 

4835 

4879 

4923 

4966 

8 

5i 

o465 

o5o8 

o552 

o595 

o639 

0682 

8 

52 

5oio 

5o54 

5o98 

5i42 

5i86 

523o 

7 

52 

O725 

o769 

0812 

0856)0899 

o943 

7 

53 

5273 

53i7 

536i 

54o5 

5449 

5493 

6 

53 

0986 

io3o 

io73 

1116 

1160 

1203 

6 

54 

5537 

558o 

5624 

5668 

5712 

5756 

5 

54 

1247 

1290 

i334 

i377 

1421 

1  464 

5 

55 

58oo 

5843 

5887 

593i 

5975 

6oi9 

4 

55 

1507 

i55i 

i594 

i638 

1681 

1725 

4 

56 

6o63 

6107 

6i5o 

6i94 

6238 

6282 

3 

56 

1768 

1811 

i855 

1898 

I942 

i985 

3 

57 

6326 

6370 

64i3 

6457 

65OI 

6545 

2 

57 

2028 

2O72 

2Il5 

2i59 

22O2 

2246 

a 

58 

6589 

6632 

6676 

6720 

6764 

6808 

I 

58 

2289 

2332 

2376 

2419 

2463 

25o6 

i 

59 

6852 

6895 

6939 

6983 

7027 

7071 

O 

59 

2549 

25g3 

2636 

2680 

2723 

2766 

o 

60" 

50" 

40" 

30" 

20" 

10" 

, 

60"     50" 

40" 

30"   20"  |  10" 

. 

Co-tangent  of  53  Degrees. 

1 

Co-tangent  of  52  Degrees. 

S 

p  p  .<  1"  2"  3"  4"  5"  6"  7"  8"  9" 

,  I"  2"  3"  4"  5"  6"  7"  8"  9" 

lrt{  4   9  13  18  22  26  31  35  40 

J.-fartj  4   9  13  17  22  26  31  35  39 

LOGARITHMIC    SINES. 


.a 

Sine  of  38  Degrees. 

_g 

Sine  of  39  Degrees. 

m 

0 

10" 

20"   30"   40"   50" 

% 

0" 

10" 

20" 

30"  |  40" 

50" 

0 

9.  789342 

9369 

9396;9423  945o'9477 

59 

O 

9.798872 

8898 

8924 

895o8976 

9002 

59 

I 

9604 

953i 

9557  9584  96i  i 

9638 

58 

I 

9028 

9064 

9o8o 

9io6  9i32 

9168 

58 

2 

9666 

9692 

97x0074607739800 

67 

2 

9184  9210 

9236 

9262  92&7 

93i3 

57 

3 

9827 

9854!988o  9907  9934  9961 

56 

3 

93399365 

939i 

94i7 

9443 

9469 

56 

4 

9988 

,.x5..4a  .,69  ..96 

.  122 

55 

4 

949519621 

9547 

9573 

9599 

9626 

55 

5 

9-79oi49 

0176:0203  O23o  0267 

0284 

54 

5 

9661 

9677 

97o3 

9728 

9754 

9-780 

54 

6 

o3io 

o337o364o39i  o4i8 

o445 

53 

6 

9806 

9832 

9858 

9884 

9910 

9936 

53 

8 

0471 
o632 

o498 
o659 

0626 
0686 

0662  0679 
071310740 

0606 
0767 

52 

5i 

8 

9962 
9.8001  17 

9987 
oi43 

oi69 

..39 
oi95 

..65 

O220 

..91 
0246 

52 
5! 

9 

0793 

08200847 

0874  0901 

0927 

5o 

9 

0272 

0298 

o324 

o35o 

o376 

o4oi 

5o 

10 

9.790954 

0981 

1008 

io34  1061 

1088 

49 

IO 

9.800427 

o453 

o479 

0606 

o53i 

o556 

49 

ii 

xxx5 

1142 

1168 

1  196 

1222 

1249 

48 

ii 

0682 

0608 

o634 

0660 

0686 

07I  I 

48 

12 

1276 

1302 

1329 

i356 

1382 

1409 

47 

12 

o737 

o763 

o789 

0816 

o84o 

0866 

47 

i3 

i436 

i463 

1489 

1616  i543 

1670 

46 

i3 

0892 

0918 

o944 

o969 

0996 

1021 

46 

i4 

i596 

1623 

i65o 

1676  1703 

1730 

45 

U 

1047 

1073 

io98 

1124 

1  160 

n76 

45 

i5 

1767 

i783 

1810 

i837 

i863 

1890 

44 

16 

1201 

1227 

1263 

I279 

i3o5 

i33o 

44 

16 

I9i7 

i943 

1970 

1997 

2024 

2060 

43 

16 

i356 

1  382 

i4o8 

1433 

i459 

i486 

43 

17 

2077 

2104 

2i3o 

2167 

2184 

22IO 

42 

17 

i5n 

1  536 

1662 

1  588 

i6i3 

i639 

42 

18 

2237 

2264 

2290  2317 

2344 

2370 

4i 

18 

1666 

1691 

1716 

1742 

i768 

i794 

4i 

19 

2397 

2423 

2460  2477 

25o3 

253o 

4o 

19 

1819 

1846 

1871 

i896 

1922 

1948 

4o 

20 
21 

9.792557 
2716 

2583 

2743 

2610  2636 
2770  2796 

2663 
2823 

2690 

2849 

39 
38 

20 

21 

9.8oi973 
2128 

1999 
2i53 

2026 

2I79 

2061 
2206 

2O76 
223O 

2102 
2256 

39 

38 

22 

2876 

29o3 

2929 

2966 

2982 

3009 

37 

22 

2282 

2307 

2333 

2359 

2384 

24lO 

37 

23 

3o35 

3o62 

3o89 

3n5 

3  1  42 

3i68 

36 

23 

2436 

2461 

2487 

2612 

2538 

2564 

36 

24 

3i95 

3222 

3248 

3275 

33oi 

3328 

35 

24 

2589 

2616 

2641 

2666 

2692 

27l8 

35 

25 

3354 

338i 

3407 

3434 

346o 

3487 

34 

25 

2743 

2769 

2794 

2820 

2846 

287I 

34 

26 

35i4 

3540 

3667 

3593 

3620 

3646 

33 

26 

2897 

2922 

2948 

2974 

2999 

3o25 

33 

27 

3673 

3699 

3726 

3752 

3779 

38o5 

32 

27 

3o5o 

3076 

3lO2 

3l27 

3i53 

3i78 

32 

28 

3832 

3858 

3885 

3911 

3938 

3964 

3i 

28 

32o4 

3229 

3255 

3281 

33o6 

3332 

3i 

29 

399i 

4oi7  4o44 

4070 

4097 

4123 

3o 

29 

3357 

3383 

34o8 

3434 

3459 

3485 

3o 

3o 
3i 

9.794i5o 
43o8 

4i7642o3 
4335436i 

4229 
4388 

4255 
44i4 

4282 
444  1 

29 

28 

3o 
3i 

9.8o35n 
3664 

3536 
3689 

3562 
37i5 

3687 
3?4o 

36i3 
3766 

3638 
379i 

29 
28 

32 

4467 

4493  4620 

4546 

4573 

4599 

27 

32 

38i7 

3842 

3868 

3893 

39i9 

3944 

27 

33 

4626 

4652  4678 

4706 

473i 

47*8 

26 

33 

397o 

3995 

4021 

4o46 

4o72 

409-7 

26 

34 

4784 

48io4837 

4863 

4890 

49i6 

25 

34 

4123 

4i48 

4i?4 

4199 

4226 

4260 

26 

35 

4942 

4969  4996 

5022 

5o48 

5o74 

24 

35 

4276 

43oi 

4327 

4352 

4377 

44o3 

24 

36 

5ioi 

5i27  5i54 

5i8o 

6206 

5233 

23 

36 

4428 

4454 

4479 

45o5 

453o 

4556 

23 

37 

5259 

6286 

53i2 

5338 

5364 

539i 

22 

3-7 

458i 

4607 

4632 

4657 

4683 

47o8 

22 

38 

54i7 

5443  547o 

5496 

5522 

5549 

21 

38 

4734 

4769 

4784 

48io 

4835 

486i 

21 

39 

5575 

56oi 

6628 

5654 

568o 

6707 

2O 

39 

4886 

49I2 

4937 

4962 

4988 

5oi3 

2O 

4o 

9.796733 

5759  5786 

6812 

5838 

5865 

I9 

4o 

9.806039 

5o64 

5o89 

5n5 

5i4o 

5i65 

J9 

4i 

6891 

59i7 

5943 

6970 

5996 

6022 

18 

4i 

6191 

6216 

6242 

6267 

6292 

53i8 

18 

42 

6049 

6o75 

6101 

6127 

6i54 

6180 

'7 

42 

5343 

5368 

5394 

5419 

5444 

547o 

17 

43 

6206 

6233 

6269 

6286 

63n 

6338 

16 

43 

5495 

6620 

5546 

557i 

5597 

6622 

16 

44 

6364 

639o64i66443 

6469 

6495 

i5 

44 

6647 

5673 

5698 

5723 

5748 

5774 

16 

45 

6621 

6547  6574  6600 

6626 

6662 

i4 

45 

6799 

6824 

585o 

5875 

6900 

6926 

i4 

46 

6679 

67o5 

673i 

6767 

6783 

6810 

i3 

46 

595i 

5976 

6002 

602-7 

6062 

6o77 

i3 

47 

6836 

6862 

6888 

69i4 

6941 

6967 

12 

47 

6io3 

6128 

6i53 

6179 

6204 

6229 

12 

48 

6993 

7oi9 

7045 

7072 

7098 

7124 

II 

48 

6264 

6280 

63o5 

633o 

6355 

638i 

II 

49 

7i5o 

7I76  7202 

7229 

7255 

7281 

IO 

49 

64o6 

643  1 

6456 

6482 

65o7 

6532 

10 

5o 

9.797307 

7333 

7359 

7386 

7412 

7438 

9 

5o 

9.  806667 

6583 

6608 

6633 

6658 

6684 

9 

5i 

7464 

749o  75i6 

7642 

7669  7595 

8 

5i 

67°9 

6734 

6759 

6785 

6810 

6835 

8 

52 

7621 

7647 

76737699 

7725  7761 

7 

62 

6860 

6885 

69n 

6936 

6961 

6986 

7 

53 

7777 

78o4 

783oJ7856  7882  7908 

6 

53 

7011 

7o37 

7062 

7o87 

7II2 

7i37 

6 

54 

7934 

796o  7986  8012  8o38  8o65 

5 

54 

7i63 

-7188 

7213 

7238 

7263 

•7288 

5 

55 
56 

57 

8091 

8247 
84o3 

8n7  8i43  8i698i95'822i 
82738299!8325835i  8377 
8429  8455  848il85o8  8534 

4 
3 

2 

55 
56 
57 

73i4 
7465 
7616 

7339 
7490 
764i 

?364 
7616 
7666 

7389 
754o 
769i 

74i4 
7565 
77i6 

7439 
-7690 
774i 

4 
3 

2 

58 

856o 

858686128638 

86648690 

I 

58 

7766  779i  78167842 

7867  7892 

I 

59 

8716 

8-742 

87688794 

8820  8846 

O 

59 

7917  7942  7967  7992  8017  8042  o 

60" 

50"  I 

40"  |  30"   20"   10" 

S" 

60"     50"  j  40"   30"   20"  i  10"   e- 

Co-sine  of  51  Degrees. 

S, 

Co'Sine  of  50  Degrees. 

S 

f  i//   nil   o/ 

P  Part) 

4"  5"  6"  7"  8"  9" 

.$  1"  2"  3"  4"  5"  6"  7"  8"  9" 

™l\  3   5   8 

11  13  16  19  21  24 

irij  3   5   8  10  13  15  18  20  23 

LOGARITHMIC    TANGENTS. 


J 

Tangent  of  38  Degrees. 

.s 

Tangent  of  39  Degrees. 

s 

0" 

10" 

20"  ]  30" 

40" 

50" 

si 

0" 

10" 

20" 

30" 

40" 

50" 

0 

9.892810 

2853 

2897 

2940 

2983 

3O27 

r 

o 

9.9o8369 

8412 

8455 

8498 

854i 

8584 

59 

I 

3070 

3u4 

3i57 

32OO 

3244 

3a87 

58 

I 

8628 

8671 

8714 

8757 

8800 

8843 

58 

2 

333i 

3374 

34i7 

346i 

35o4 

3547 

57 

2 

8886 

8929 

8972 

9oi5 

9o58 

9101 

$7 

3 

359i 

3634 

3678 

3721 

3764 

38o8 

56 

3 

9i44 

9187 

9230 

9273 

93i6 

9359 

56 

4 

385i 

3894 

3938 

398i 

4o25 

4o68 

55 

4 

9402 

9445 

9488 

953i 

9574 

96l7 

55 

5 

4i  1  1 

4i55 

4198 

4241 

4285 

4328 

54 

5 

9660 

97°3 

9746 

9789 

9832 

9875 

54 

6 

4372 

44i5 

4458 

45o2 

4545 

4588 

53 

6 

9918 

9961 

...5 

..48 

..9i 

.i34 

53 

7 

4632 

4675 

47i8 

4762 

48o5 

4848 

52 

7 

9.910177 

O220 

0263 

o3o6 

o349 

o392 

52 

8 

4892 

4935 

4979 

5022 

5o65 

5  1  09 

5i 

8 

o435 

0478 

O52I 

o564 

0607 

o65o 

5i 

9 

5i52 

5i95 

5239 

5282 

5325 

5369 

5o 

9 

0693 

o736 

°779 

0822 

o865 

o9o8 

5o 

10 

9.895412 

5455 

5499i5542 

5585 

5629 

49 

10 

9.910951 

0994 

1037 

1080 

1123 

1  166 

4y 

ii 

5672 

57i5 

5759 

58o2 

5845 

5889 

48 

ii 

1209 

1252 

I295 

i338 

i38i 

i424 

48 

12 

5932 

5975 

6oi9 

6062 

6io5 

6149 

47 

12 

1467 

i5io 

i553 

i596 

i639 

1682 

47 

i3 

6192 

6235 

6278 

6322 

6365 

64o8 

46 

i3 

1725 

1768 

1810 

i853 

i896 

i939 

46 

i4 

6452 

6495 

6538 

6582 

6625 

6668 

45 

i4 

1982 

2025 

2068 

21  II 

2i54 

2I97 

45 

15 

6712 

6755 

6798 

6842 

6885 

6928 

44 

i5 

2240 

2283 

2326 

2369|24l2 

2455 

44 

16]    6971 

7Oi5 

7o58 

7101 

7i45 

7188 

43 

16 

2498 

254i 

2584 

2627]2670 

2713 

43 

17 

7231 

7275 

73i8 

736i 

74o4 

7448 

42 

I? 

2756 

2799 

2842 

26862928 

297I 

42 

18 

7491 

?534 

7578 

7621 

7664 

7707 

4i 

18 

3oi4 

3o57 

3ioo 

3i43 

3i85 

3228 

4i 

*9 

775i 

7794 

7837 

7881 

7924 

7967 

4o 

J9 

3271 

33i4 

3357 

34oo 

3443 

3486 

4o 

20 

9.898010 

8o54 

8o97 

8i4o 

8i83 

8227 

39 

20 

9.913529 

3572 

36i5 

3658 

3701 

3744 

39 

21 

8270 

83i3 

8357 

84oo 

8443 

8486 

38 

21 

3787 

383o 

3873 

39i6 

3959 

4ooi 

38 

22 

853o 

8573 

8616 

8659 

87o3 

8746 

37 

22 

4o44 

4o87 

4i3o 

4i73 

4216 

4259 

37 

23 

8789 

8832 

8876 

8919 

8962 

gooS 

36 

23 

4302 

4345 

4388 

443  1 

4474 

45i7 

36 

24 

9049 

9092 

9i35 

9178 

9222 

9265 

35 

24 

456o 

46o3 

4645 

4688 

473i 

4774 

35 

25 

9308 

935i 

9395 

9438 

948i 

9524 

34 

25 

48i7 

486o 

49o3 

4946 

4989 

5o32 

34 

26 

9568 

9611 

9654 

9697 

974i 

9784 

33 

26 

5o75 

5ii8 

5i6i 

52o3 

5246 

5289 

33 

27 

0827 

0870 

QQl4 

QC)57 

43 

32 

27 

5332 

5375 

54i8 

546  1 

55o4 

5547 

32 

*  / 
28 

v  / 
9.900087 

v  / 
oi3o 

yy.n4 
0173 

77  / 
02l6 

0259 

o3o3 

3i 

*  1 
28 

559o 

5633 

5675 

57i8 

5761 

vs^x  44.  i 

58o4 

3i 

20 

o346 

o389 

0432 

0476 

o5i9 

o562 

3o 

29 

5847 

5890 

5933 

5976 

6019 

6062 

3o 

3o 

9.900605 

o648 

o692 

o735 

0778 

0821 

29 

3o 

9.916104 

6i47 

6i9o 

6233 

6276 

63I9 

29 

3i 

0864 

o9o8 

o95i 

0994 

1037 

1081 

28 

3i 

6362 

64o5 

6448 

649i 

6533 

6576 

28 

32 

1124 

1167 

I2IO 

1253 

I297 

i34o 

27 

32 

6619 

6662 

6705 

6748 

6791 

6834 

27 

33 

i383 

1426 

i469 

i5i3 

i556 

i599 

26 

33 

6877 

6919 

6962 

7005 

7o48 

7091 

26 

34 

1642 

i685 

T729 

1772 

i8i5 

i858 

25 

34 

7i34 

7177 

7220 

7262 

73o5 

7348 

25 

35 

1901 

i944 

i988 

2031 

2074 

2117 

24 

35 

739i 

7434 

7477 

7520 

7563 

76o5 

24 

36 

2160 

2204 

2247 

2290 

2333 

2376 

23 

36 

7648 

7691 

7734 

7777 

7820 

7863 

23 

3? 

2420 

2463 

25o6 

2549 

2592 

2635 

22 

37 

7906 

7948 

799  l 

8o34 

8077 

8120 

22 

38 

2679 

2722 

2765 

2808 

285i 

2894 

21 

38 

8i63 

8206 

8248 

820.1 

8334 

8377 

21 

39 

2938 

298i 

3o24 

3o67 

3no 

3i53 

2O 

39 

8420 

8463 

85o6 

8548 

8591 

8634 

2O 

4o 

9.903197 

324o 

3283 

3326 

3369 

34i2 

I9 

4o 

9.918677 

8720 

8763 

88o5 

8848 

889i 

T9 

4i 

3456 

3499 

3542 

3585 

3628 

367i 

18 

4i 

8934 

8977 

9020 

9o63 

9io5 

9i48 

18 

42 

37i4 

3758 

38oi 

3844 

3887 

393o 

I7 

42 

9191 

9234 

9277 

9320 

9362 

94o5 

11 

43 

3973 

4oi6 

4o6o 

4io3 

4i46 

4i89 

16 

43 

9448 

9491 

9534 

9577 

9619 

9662 

16 

44 

4232 

4275 

43i8 

4362 

44o5 

4448 

i5 

44 

9705 

9748 

9791 

98S4 

9876 

99i9 

i5 

45 

449i 

4534 

4577 

4620 

4663 

4707 

i4 

45 

9962 

...5 

.  48 

..9i 

.i33 

.  176 

i4 

46 

475o 

4793 

4836 

4879 

4922 

4965 

i3 

46 

9.920219 

0262 

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o348 

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o433 

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4? 

5oo8 

5o52 

5o95 

5i38 

5i8i 

5224 

12 

47 

0476 

oSig 

0062 

o6o4 

0647 

0690 

12 

48 

5267 

53io 

5353 

5397 

544o 

5483 

II 

48 

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0947 

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49 

5526 

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5655 

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574i 

10 

49 

0990 

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1075 

1118 

1  161 

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5o 

9.905785 

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5871 

59i4 

5957 

6000 

9 

5o 

9.921247 

1289 

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i375 

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9 

5i 

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6172 

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8 

5i 

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1  546 

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i632 

i675 

1717 

8 

52 

63o2 

6345 

6388 

643i 

6474 

65i7 

7 

52 

1760 

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i846 

i889 

1931 

i974 

7 

53 

656o 

66o3 

6646 

6690 

6733 

6776 

6 

53 

2017 

2060 

2103 

2i45 

2188 

223l 

6 

54 

6819 

6862 

6905 

6948 

6991 

7034 

5 

54 

2274 

23i6 

2359 

2402 

2445 

2488 

5 

55 

7077 

7120 

7i63 

7207 

725o 

7293 

4 

55 

253o 

2573 

2616 

2659 

2702 

2744 

4 

56 

7336 

7379 

7422 

7465 

75o8 

755i 

3 

56 

2787 

283o 

2873 

29l5 

2958 

3ooi 

3 

5? 

7594 

7637 

7680 

7723 

7766 

78o9 

2 

57 

3o44 

3087 

3i29 

3172 

32i5 

3258 

2 

58 

7853 

7896 

7939 

7982 

8025 

8068 

I 

58 

33oo 

3343 

3386 

3429 

347i 

35i4 

I 

59 

Bin 

8i54 

8i97 

8240 

8283 

8326 

0 

59 

3557 

36oo 

3642 

3685 

3728 

377i 

O 

60" 

50" 

40" 

30" 

20" 

10" 

CJ 

60"     50" 

40" 

30" 

20" 

10" 

j 

Co-tangent  of  5  1  Degrees. 

s 

Co-tangent  of  50  Degrees. 

s 

p  pa%t  5  *"  2"  3"  4"  5"  6//  7"  8//  9" 

.  <  I"  2"  3"  4"  5"  6"  7"  8"  9" 

1   lrl{  4   9  13  17  22  26  30  35  39 

irt\  4   9  13  17  21  26  30  34  39 

64 


LOGARITHMIC    SINES. 


g- 

Sine  of  40  Degrees. 

J 

Sine  of  41  Degrees. 

5 

0" 

10"   20" 

!  30"   40" 

50" 

S 

0" 

10" 

20" 

30"  |  40" 

50" 

0 

9.  808067 

8o93  8u88i43  8168 

8i93 

59 

O 

9.8i6943 

6967 

6991 

70l6 

7o4o 

7o64 

59 

I 

8218 

824382688293:83188343 

58 

I 

•7088 

7I  12 

7i37 

-7161 

7i85 

-7209 

58 

2 

8368 

8393  8419  8444  8469  8494 

57 

2 

7233 

7258 

7282 

73o6 

733o 

7354 

57 

3 

85i9 

8544  8569859^  8619  8644 

56 

Q 

7379 

74o3 

7427 

745i 

7475 

7499 

56 

4 

8669 

8694  8-719  8744.8769 

8794 

55 

l\ 

7524 

7548 

75?2 

7596 

-7620 

7644 

55 

5 

8819 

8844886988948919 

8944 

54 

5 

-7668 

7693 

7717 

774i 

7765 

7789  54 

6 

8969 

8994  9019  9044  9069  9o94 

53 

6 

78i3 

7837 

7862 

7886 

7910 

7934)53 

7 

9119 

9144  9169  9194  9219  9244 

52- 

7 

7958 

-7982 

8006 

8o3o 

8o55 

8o79 

52 

8 

9269 

9294  9319  9344  9369  9394 

5i 

8 

8io3 

812-7 

8i5i 

8i75 

8199 

8223 

5i 

9 

9419 

9444  9469  9494  95i9  9544 

5o 

9 

8247 

8272 

8296 

8320 

8344 

8368 

5o 

10 

9.809569 

9594  9619  9643:9668  9693 

49 

10 

9.818392 

84i6 

844o 

8464 

8488 

85i2 

49 

ii 

9718 

9743  9768 

9793  98i8 

9843 

48 

ii 

8536 

856o 

8584 

86o9 

8633 

8657 

48 

12 

i3 

9868 
9.810017 

9893  9918  9943'9967 
0042  oo67  0092;©!  1  7 

9992 

Ol42 

47 
46 

12 

i3 

8681 
8825 

87o5 
8849 

8729 
8873 

8753 
8897 

8777 
8921 

8801 
8945 

47 
46 

i4 

0167 

0191  O2l6tO24l 

0266 

0291 

45 

i4 

8969 

8993 

9017 

9041 

9065 

9089 

45 

i5 

o3i6 

634xo366 

o39o  o4i5 

o44o 

44 

i5 

9113 

9i37 

9161 

9i85 

9209 

9233 

44 

16 

o465 

0490  o5i5 

o54o  o564 

o589 

43 

16 

9257 

9281 

93o5 

9329 

9353 

9377 

43 

17 

0614 

06390664 

0689 

o7i3 

o738 

42 

17 

94oi 

9425 

9449 

9473 

9497 

9521 

42 

18 

o763 

078808*3 

o838 

0862 

o887 

4i 

18 

9545 

9569 

9593 

96i7 

9641 

9665 

4i 

*9 

0912 

093-7  0962 

0986 

ion 

io36 

4o 

'9 

9689 

97i3 

9737 

976i 

9785 

9809 

4o 

20 

9  811061 

1086  mo 

n35 

1  1  60 

u85 

39 

20 

9.819832 

9856 

9880 

99o4 

9928 

9952 

39 

21 

1210 

1234  1259 

1284 

1  309 

1  334 

38 

21 

9976 

.  .  .  . 

..24 

..48 

..72 

..96 

38 

22 

i358 

i383  i4o8 

i433 

i457 

1482 

37 

22 

9.820120 

oi43 

oi67 

oi9i 

02l5 

0239 

37 

23 

1507 

i532i556 

i58i 

1606 

i63i 

36 

23 

0263 

028-7 

o3n 

o335 

0359 

o382 

36 

24 

i655 

1680  I7o5 

i73o 

i754 

i779 

35 

24 

o4o6 

o43o 

o454 

o478 

o5o2 

o526 

35 

25 
26 

1804 
1952 

1828  i853'i878 
19-7-7  200112026 

1903 
2o5i 

1927 
20-76 

34 
33 

25 

26 

o55o 
0693 

o573 

07I7 

o597 
o74o 

0621 
o764 

0645 

o788 

0669 
0812 

34 
33 

27 
28 

2IOO 

2248 

2125  2l5o!2I74 
2273  2298;2322 

2199  2224 

2347J2372 

32 

3i 

27 

o836 
°979 

0860 
ioo3 

o883 
1026 

090-7 
io5o 

0931 
io74 

o955 
io98 

32 

3i 

»9 

2396 

2421  2446  2470 

2495  J252O 

3o 

29 

1122 

n46 

1  169 

n93 

I2I7 

1241 

3o 

3o 

Q.  812544 

2569  2594  2618 

26432668 

29 

3o 

9.821265 

1288 

l3l2 

i336 

i36o 

1  384 

29 

3i 

2692 

27I7  2742 

2766 

2791  28i5 

28 

3i 

i4o7 

i43i 

i455 

1479 

i5o2 

i526 

28 

32 

2840 

2865  2889  2914 

2939  2963 

27 

32 

i55o 

i574 

i598 

1621 

i645 

1669 

27 

33 

2988 

3oi2  3o37 

3o62 

3o86 

3m 

26 

33 

1693 

1-716 

i74o 

i764 

i  -788 

1811 

26 

34 

3i35 

3!6o3i85 

3209 

3234 

3258 

25 

34 

i835 

1869 

i883 

1906 

1930 

1954 

25 

35 

3283 

33o733323357 

338i 

34o6 

24 

35 

I977 

2001 

2025 

2049 

20-72 

2096 

24 

36 

343o 

3455  3479  35o4 

3529!3553 

23 

36 

ei2o 

2i44 

216-7 

2191 

22l5 

2238 

23 

37 

3578 

36o2  3627 

365i 

3676 

37oo 

22 

37 

2262 

2286 

2309 

2333 

2357 

2  38  1 

22 

38 

3725 

3749  3774 

3799 

3823 

3848 

21 

38 

2404 

2428 

2452 

2475 

2499 

2523 

21 

39 

3872 

389-73921 

3946 

3970  3995 

2O 

39 

2546 

257O 

2594 

261-7 

2641 

2665 

2O 

4o 

9.814019 

4o44  4o68 

40934117 

4142 

'9 

4o 

9.822688 

27I2 

2736 

2759 

2783 

280-7 

19 

4i 

4i66 

4191  42i5 

424042644289 

18 

4i 

283o 

&854 

2878 

2901 

2925 

2948 

18 

42 

43x3 

43384362|4387|44n 

4436 

i7 

42 

2972 

2996 

3oi9 

3o43 

3o67 

3o9o 

17 

43 

446o 

4484  45o9 

4533 

45584582 

16 

43 

3n4 

3i37 

3i6i 

3i85 

32o8 

3232 

16 

44 

46o7 

463i  4656 

468o 

47044729 

i5 

44 

3255 

3279 

33o3 

3326 

335o 

3373 

i5 

45 

4753 

477848o2 

482-7 

485  1 

4876 

i4 

45 

3397 

342i 

3444 

3468 

3491 

35i5 

i4 

46 

4900 

4924  4949 

4973 

4998 

5022 

i3 

46 

3539 

3562 

3586 

3609 

3633 

3656 

i3 

47 

5o46 

5o7i  6095 

5l20 

5i44 

5i68 

12 

47 

368o 

37o4 

3727 

375i 

3774 

3798 

12 

48 
49 

5i93 
5339 

52I7  5242  5266 

53645388|54i2 

5290 
5437 

53i5 
546i 

II 
IO 

48 
49 

382i 
3963 

3845 
3986 

3868 
4oio 

3892 
4o33 

39i5 
4o57 

3939 
4o8o 

II 
IO 

5o 

9.8i5485 

55io5534i5558 

5583 

5607 

9 

5o 

9.824104 

412-7 

4i5i 

4i74 

4198 

4221 

9 

5i 

5632 

5656  568o  57o5 

5729  5753 

8 

5i 

4245 

4268 

4292 

43i5 

4339 

4362 

8 

52 

5778 

58o2  5826 

585i 

5875 

589Q 

7 

52 

4386 

4409 

4433 

4456 

448o 

45o3 

7 

53 

54 

5924 
6069 

5g48  59-72  599616021  6o45 
609461186142  616-76191 

6 
5 

53 

54 

4527 
4668 

455o 
469i 

4574 

4597 
4738 

4621 
476i 

4644 
4785 

6 
5 

55 

62i5 

6240  6264  6288:6312  6337 

4 

55 

48o8 

4832 

4855 

4879 

4902 

4926 

4 

56 

636i 

6385  64o9'6434  6458  6482 

3 

56 

4949 

4972 

4996 

5o43 

5o66 

3 

57 
58 
59 

65o7 
6652 
6798 

653i.6555j6579  66o4  6628 
6676  67oi  6725i6749  6773 
6822  6846  687016894  6919 

2 

I 
O 

57 
58 
59 

5090 
523o 
537i 

5n3 
5254 
5394 

5i36 

5277 

54i7 

5i6o 
53oo 

544i 

5i83 
5324 
5464 

52O7 

5347 

5488 

2 
I 
O 

60" 

50"  ;  40" 

30"  |  20"  , 

10" 

c 

60" 

50"  j  40" 

30" 

20" 

10" 

fl 

Co-sine  of  49 

Degrees. 

1 

Co-sine  of  48  Degrees. 

P.  Part  J  2   5   7  10 

5"  6"  7" 
12  15  17 

8"  9" 
20  22 

p  p  .  $  1"  2"  3"  4"  5"  6"  7"  A"  9" 
r*\  25   7  10  12  14  17  19  21 

LOGARITHMIC    TANGENTS. 


.5 

Tangent  of  40  Degrees. 

.S 

Tangent  of  41  Degrees. 

i 

0" 

10" 

20" 

30" 

40"   50" 

i 

0" 

10" 

20" 

30" 

40" 

50" 

o 

9.923814 

3856 

3899 

3942 

3985 

4027 

59 

o 

9.939163 

9206 

9248 

9291 

9333 

9376 

59 

i 

4070 

4n3 

4i56 

4198 

424i 

4284 

58 

I 

94i8 

946  1 

95o3 

9546 

9588 

963i 

58 

2 

4327 

4369 

44i2 

4455 

4498 

4540 

57 

2 

9673 

9716 

9758 

9801 

9843 

9886 

57 

3 

4583 

4626 

4669 

4711 

4754 

4797 

56 

3 

9928 

9971 

..i3 

..56 

..98 

.141 

56 

4 

484o 

4882 

4925 

4968 

Son 

5o53 

55 

4 

9.940183 

0226 

0268 

o3n 

o354 

o396 

55 

5 

5o96 

5  1  39 

5i8i 

5224 

526-7 

53io 

54 

5 

0439 

o48i 

o524 

o566 

0609 

o65i 

54 

6 

5352 

5395 

5438 

5481 

5523 

5566 

53 

6 

0694 

o736 

0779 

0821 

o864 

0906 

53 

7 

5609 

5652 

56g4 

5737 

578o 

5822 

52 

7 

0949 

0991 

io34 

io76 

1119 

1161 

52 

8 

5865 

5908 

595i 

5993 

6o36 

6o79 

5i 

8 

1204 

1246 

1289 

i33i 

i374 

i4i6 

5i 

9 

6122 

6i64 

6207 

6260 

6292 

6335 

5o 

9 

i459 

i5oi 

1  544 

i586 

1628 

16-71 

5o 

10 

9.926378 

6421 

6463 

65o6 

6549 

659i 

49 

IO 

9.941713 

1-756 

1798 

i84i 

i883 

1926 

49 

ii 

6634 

6677 

672O 

6-762 

68o5 

6848 

48 

ii 

1968 

2011 

2o53 

2096 

2i38 

2181 

48 

12 

6890 

6933 

697e 

7oi9 

-7061 

7io4 

47 

12 

2223 

2266 

23o8 

235i 

2393 

2436 

47 

i3 

7147 

7189 

7232 

7275 

73i7 

736o 

46 

i3 

2478 

2521 

2563 

2606 

2648 

2691 

46 

i4 

74o3 

7446 

7488 

753i 

7574 

76i6 

45 

i4 

2733 

2776 

2818 

286! 

2903 

2945 

45 

i5 

7669 

7702 

7744 

7787 

783o 

7872 

44 

i5 

2988 

3o3o 

3o73 

3n5 

3i58 

3200 

44 

16 

7915 

7958 

8001 

8o43 

8086 

8129 

43 

16 

3243 

3285 

3328 

337o 

34i3 

3455 

43 

I7 

8171 

8214 

8257 

8299 

8342 

8385 

42 

I7 

3498 

354o 

3583 

3625 

3667 

3-710 

42 

18 

8427 

8470 

85i3 

8555 

8598 

864i 

4i 

18 

3752 

3795 

3837 

388o 

3922 

3965 

4i 

J9 

8684 

8726 

8769 

8812 

8854 

8897 

4o 

*9 

4oo7 

4o5o 

4092 

4i35 

4i77 

4219 

4o 

20 

9.928940 

8982 

9025 

9o68 

9no 

9i53 

39 

20 

9.944262 

43o4 

4347 

4389 

4432 

4474 

39 

21 

9196 

9238 

9281 

9324 

9366 

9409 

38 

21 

45i7 

4559 

4602 

4644 

4686 

4-729 

38 

22 

9452 

94g4 

9537 

958o 

9622 

9665 

37 

22 

«  477i 

48i4 

4856 

4899 

494i 

4984 

37 

23 

9708 

975o 

9793 

9836 

9878 

9921 

36 

23 

5o26 

5o69 

5m 

5i53 

5196 

5238 

36 

24 

9964 

...6 

..49 

..92 

.134 

.177 

35 

24 

5281 

5323 

5366 

54o8 

545i 

5493 

35 

25 

9.930220 

0262 

o3o5 

o348 

0390 

o433 

34 

25 

5535 

5578 

562O 

5663 

57o5 

5748 

34 

26 

o475 

o5i8 

o56i 

o6o3 

0646 

0689 

33 

26 

5790 

5832 

5875 

59i7 

5960 

6002 

33 

2? 

«o73i 

0774 

o8i7 

o859 

0902 

o945 

32 

27 

6o45 

6087 

6i3o 

61-72 

6214 

6257 

32 

28 

0987 

io3o 

io73 

in5 

n58 

1  200 

3i 

28 

6299 

6342 

6384 

6427 

6469 

65n 

3i 

29 

1243 

1286 

i328 

i37i 

i4i4 

i456 

3o 

29 

6554 

6596 

6639 

6681 

6-724 

6766 

3o 

3o 

9.931499 

1  542 

i584 

162-7 

1669 

1712 

29 

3o 

9.9468o8 

685i 

6893 

6936 

6978 

-7021 

29 

3i 

i755 

1797 

i84o 

i883 

1925 

1968 

28 

3i 

7o63 

7io5 

7i48 

7i9o 

7233 

7275 

28 

32 

2010 

2o53 

2096 

2i38 

2181 

2224 

27 

32 

73i8 

736o 

7402 

7445 

7487 

753o 

27 

33 

2266 

2309 

235i 

2394 

2437 

2479 

26 

33 

7572 

7614 

7657 

7699 

7742 

7784 

26 

34 

2522 

2565 

2607 

265o 

2692 

2735 

25 

34 

7827 

7869 

7911 

7954 

7996 

8o39 

25 

35 

2778 

2820 

2863 

29o6 

2948 

2991 

24 

35 

8081 

8i23 

8166 

8208 

825i 

8293 

24 

36 

3o33 

3o76 

3n9 

3i6i 

3204 

3246 

23 

36 

8335 

8378 

8420 

8463 

85o5 

8548 

23 

37 

3289 

3332 

3374 

34i7 

3459 

35o2 

22 

37 

8590 

8632 

8675 

87i7 

876o 

8802 

22 

38 

3545 

3587 

363o 

3672 

37i5 

3758 

21 

38 

8844 

8887 

8929 

8972 

9oi4 

9o56 

21 

39 

38oo 

3843 

3885 

3928 

397i 

4ot3 

20 

39 

9099 

9i4i 

9i84 

9226 

9268 

g3ii 

2O 

4o 

9.934o56 

4o98 

4i4i 

4i84 

4226 

4269 

X9 

4o 

9.949353 

9396 

9438 

948o 

9523 

9565 

'9 

4i 

43n 

4354 

4397 

4439 

4482 

4524 

18 

4i 

9608 

965o 

9692 

9735 

9777 

9819 

18 

42 

4567 

46io 

4652 

4695 

4737 

478o 

J7 

42 

9862 

99o4 

9947 

9989 

..3i 

..74 

«7 

43 

4822 

4865 

49o8 

495o 

4993 

5o35 

16 

43 

9.95oii6 

oi59 

O2OI 

0243 

0286 

o328 

16 

44 

5o78 

5l2I 

5i63 

5206 

5248 

5291 

i5 

44 

o37i 

o4i3 

o455 

0498 

o54o 

o582 

i5 

45 

5333 

5376 

54i9 

546i 

55o4 

5546 

i4 

45 

0625 

0667 

0-710 

O752 

0794 

o837 

i4 

46 

5589 

5632 

5674 

57i7 

5759 

58o2 

i3 

46 

0879 

0921 

0964 

1006 

1049 

1091 

i3 

47 

5844 

5887 

5930 

5972 

6oi5 

6o57 

12 

4? 

1x33 

1176 

1218 

1261 

i3o3 

1  345 

12 

48 

6100 

6142 

6i85 

622-7 

62-70 

63i3 

II 

48 

i388 

i43o 

1472 

i5i5 

i557 

1600 

II 

49 

6355 

6398 

644o 

6483 

6525 

6568 

IO 

49 

1  642 

1  684 

I727 

i769 

1811 

i854 

IO 

5o 

9.936611 

6653 

6696 

6738 

678i 

6823 

9 

5o 

9.951896 

1938 

1981 

2023 

2066 

2108 

9 

5i 

6866 

6908 

6951 

6994 

7o36 

7°79 

8 

5i 

2i5o 

2193 

2235 

2277 

2320 

2362 

8 

52 

7121 

7i64 

72o6 

7249 

729I 

7334 

7 

52 

24o5 

2447 

2489 

2532 

2574 

2616 

7 

53 

7377 

•7419 

7462 

75o4 

7547 

7589 

6 

53 

2659 

2701 

2743 

2786 

2828  28-70 

6 

54 

7632 

7674 

77I7 

7759 

7802 

7845 

5 

54 

2913 

2955 

2998 

3o4o 

3o82»3i25 

5 

55 

7887 

793o 

7972 

8oi5 

8o57 

8100 

4 

55 

3i67 

3209 

3252 

3294 

3336!3379 

4 

56 

8142 

8i85 

822-7 

82-70 

83i2 

8355 

3 

56 

342i 

3463 

35o6 

3548 

359i|3633 

3 

57 

8398 

844o 

8483 

8525 

8568 

8610 

2 

57 

3675 

37i8 

376o 

3802 

3845J3887 

2 

58 

8653 

8695 

8738 

878o 

8823 

8865 

I 

58 

3929 

3972 

4oi4 

4o56 

4099  4i4i 

I 

5q 

8908 

895o 

8993 

9o35 

9o78 

9121 

O 

59 

4i83 

4226 

426843io|4353!4395 

O 

60" 

50" 

40" 

30"   20" 

10" 

. 

60"     50" 

40"   30"   20"   10" 

a 

Co-tangent  of  49  Degrees. 

a 

Co-tangent  of  48  Degrees. 

i 

.<  1"  2"  3"  4"  5"  6"  7"  8"  9" 

.<  1"  2"  3"  4"  5"  6"  7"  8"  9" 

in\  4  9  13  17  21  26  30  34  38 

in\  4  8  13  17  21  25  30  34  38 

E 


66 


LOGARITHMIC    SINES. 


c 

Sine  of  42  Degrees. 

S 

Sine  of  43  Degrees. 

i 

0" 

10" 

20" 

30" 

40"  !  50" 

S 

0"    I  10" 

20" 

30" 

40" 

50" 

O  9.8255l  I 

5534 

5558558i 

56o45628 

9 

0 

9.833783  38o6 

828 

385i 

3874 

3896 

59 

I 

565i 

56?  5 

5698  572i 

5745;5768 

8 

I 

39i9 

94i 

964 

3986 

4oo9 

4o32 

58 

2 

579i  58i5 

5838586i 

5885  59o8 

7 

2 

4o54 

4077 

°99 

4l22 

4x44 

4i67 

57 

3 

593! 

5955 

6978  6001 

6o25  6o48 

6 

3 

4i89 

212 

4234 

4257 

4280 

43o2 

56 

4 

6071 

6095 

6n86i4i 

6i656i88 

5 

4 

4325 

4347 

37o 

4392 

44i5 

4437 

55 

5 

6211 

623562686281 

63o56328 

4 

5 

446o 

4482 

5o5 

4527 

455o 

4572 

54 

6 

635i  63756398642i 

6444:6468 

3 

6 

4595 

46i7 

464o 

4662 

4685 

4707 

53 

7 

649i  65i4 

6538656i 

6584,66o7 

2 

7 

473o 

.752 

4775 

4797 

4820 

4842 

52 

8 

663i  6654 

6677  6701 

6724*6747 

I 

8 

4865 

.887 

910 

4954 

4977 

5i 

9 

6770 

679468176840 

6863  6887 

0 

9 

4999 

5O22 

o44 

5o67 

5o89 

5lI2 

5o 

10 

9.826910 

6933 

6966  6980 

7oo3  7026 

9 

10 

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5!57 

i79 

52OI 

5224 

5246 

49 

ii 

7o49 

7o73 

7096  7119 

7142  7165 

8 

ii 

5269 

529I 

3i4 

5336 

5358 

538i 

48 

12 

7i89 

72I2 

7235  7258 

7282  73o5 

,7 

12 

54o3 

54.16 

5448 

5471 

5493 

55i5 

47 

i3 

7328 

735i 

7374  7398 

7421 

7444 

46 

i3 

5538 

556o 

5583 

56o5 

5627 

565o 

46 

i4 

7467 

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7614  7537 

75607583 

45 

i4 

5672 

5695 

57i7 

5739 

5762 

5784 

45 

i5 

7606 

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7653  7676 

7699  7722 

44 

i5 

58o7 

5829 

585i 

5874 

5896 

59i8 

44 

16 

7745 

7768 

7792  7815 

7838,7861 

.3 

16 

594i 

5963 

5986 

6008 

6o3o 

6o53 

43^ 

17 

7884 

7907 

793i  7954 

79778000 

.2, 

ll 

6o75 

6o97 

6120 

6142 

6i64 

6187 

42 

1  8 

8o23 

8o46 

$069 

BogS 

I 

18 

6209 

623i 

6254 

6276 

6298 

632i 

4i 

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8162 

8i85 

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82548278 

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6343 

6365 

6388 

64  10 

6432  6455 

4o 

20 

9.  8283oi 

8324 

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20 

9.836477 

6499 

6522 

65446566 

6589 

39 

21 

8439 

8462 

8485  85o9 

85328555 

38 

21 

6611 

6633 

6656 

6678  6700 

6722 

38 

22 

8578 

8601 

86248647 

86708^93 

37 

22 

6745 

6767 

6789 

6812 

6834 

6856 

37 

23 

8716 

8739 

87628786 

88098832 

36 

23 

6878 

69oi 

6923 

6945 

6968 

6990 

36 

24 

8855 

8878 

89oi  8924 

8947  8970 

35 

24 

7012 

7o34 

7o57 

7079 

7IOI 

7123 

35 

25 

6993 

9016 

9o39  9o62 

9085  9108 

34 

25 

7i46 

7168 

7190 

7212 

7235 

7257 

34 

26 

9i3i 

9i54 

9i77920o 

9223  9246 

33 

26 

7279 

73oi 

7324 

7346 

7368 

739° 

33 

27 

9269 

9292 

93i59338936i 

9384 

32 

27 

7412 

7435 

7457 

7479 

75oi 

^524 

32 

28 

94o7 

943o 

9453  9476  9499 

9522 

3i 

98 

7546 

7568 

7^9° 

7612 

7635 

7657 

3i 

29 

9545 

9568 

9691  9614 

96379660 

3o 

29 

7679 

7701 

7723 

7746 

7768 

779° 

3o 

3o 

9.829683 

97o6 

97299752 

97759798 

29 

3o 

9.837812 

7834 

7857 

7879 

7901 

7923 

29 

3i 

982I 

9844 

9867  9890 

99i3 

9936 

28 

3i 

7945 

7967 

799° 

8012 

8o34 

8o56 

28 

32 

9959 

9982 

...5 

..28 

..74 

27 

32 

8078 

8100 

8i23 

8i45 

8167 

8i89 

27 

33 

9.83oo97 

0120 

0142  oi65 

0188 

0211 

26 

33 

8211 

8233 

8256 

8278  83oo 

8322 

26 

34 

0234 

0267 

0280  o3o3 

o326 

0349 

25 

34 

8344 

8366 

8388 

84io 

8433 

8455 

25 

35 

0372 

o395 

0417  o44o 

o463 

o486 

24 

35 

8477 

8499 

852i 

8543 

8565 

8587 

24 

36 

o5o9 

o532 

o555 

0678 

0601 

0624 

23 

36 

8610 

8632 

8654 

8676 

8698 

8720 

23 

37 

o646 

o669 

0692  0715 

o738 

0761 

22 

37 

8742 

8764 

8786 

8808 

883i 

8853 

22 

38 

0784 

0807 

0829 

o852 

o875 

o89S 

21 

38 

8875 

8897 

8919 

894i 

8963 

8985 

21 

39 

O92I 

o944 

0967  0989 

1012 

io?5 

20 

39 

9007 

9029 

9o5i 

9o73 

9o95 

9n8 

2O 

4o9.83io58 

1081 

no4 

1127 

n49 

1  172 

19 

4o 

9.839140 

9162 

9182 

92o6 

9228 

925o 

19 

4i 

1195 

1218 

1241 

1263 

1286 

i3o9 

18 

4i 

9272 

9294 

9316 

9338 

936o 

9382 

18 

42 

1332 

i355 

i378 

i4oo 

i423 

1  446 

17 

42 

9404 

9426 

9448 

947o 

9492 

g5i4 

!• 

43 

i469 

l492 

i5i4 

i537 

i56o 

i583 

16 

43 

9536 

9558 

958o 

96o2 

9624 

9646 

It 

44 

1606 

1628 

i65i 

i674 

i697 

1720 

i5 

44 

9668 

9690 

9712 

9734 

9756 

9778 

i5 

45 

1742 

1765 

1788 

1811 

i833 

i856 

i4 

45 

9800 

9822 

9844 

9866 

9888  9910 

i4 

46 

i879 

1902 

1924 

194-7 

i97o 

i993 

i3 

46 

9932 

9954 

9976 

9998 

.  .20  .  .42 

i3 

47 

20l5 

2o38 

2061 

2084 

2106 

2129 

12 

4? 

9.84oo6/! 

0086 

0108 

Ol52 

O\n£ 

12 

48 

2l52 

2I75 

2197 

222O 

2243 

2266 

II 

48 

0196 

0218 

0240 

0262 

0284 

o3o6 

II 

49 

2288 

23ll 

23342356 

2379 

2402 

IO 

49 

o328 

o35o 

0372 

o393 

o4i5 

o437 

10 

5o9.  832425 

2447 

2470 

2493 

25i5 

2538 

9 

5o 

9.840459 

o48i 

o5o3 

o525 

o54y 

o569 

9 

5i 

256i 

2584 

2606 

2629 

2652 

2674 

8 

5i 

oSgi 

06  1  ^ 

o635 

o657 

0678 

0700 

8 

52 

2697 

2720 

2742 

2765 

2788 

2810 

7 

52 

0722 

074^ 

0766 

0-7880810 

o832 

7 

53 

2833 

2856 

2878 

2901 

2924 

2946 

6 

53 

o854 

0876 

0897 

0919  0941 

o963 

6 

54 

2969 

2992 

3oi4 

3o37 

3o6o 

3082 

5 

54 

0985 

1007 

1029 

io5i 

1072 

109^ 

5 

55 

3io5 

3i28 

3i5o 

3i73 

3I96 

32i8 

4 

55 

1116 

n38 

1  1  60 

1182  \izoi 

1226 

4 

56 

3s4  i 

3263 

3286 

3309 

333i 

3354 

3 

56 

1247 

1269 

1291 

i3i3  i335 

i357 

3  , 

57 

3377 

3399 

3422 

3444 

3467 

349o 

2 

57 

i378 

i4oo 

1422 

i444i466 

i486 

58 

35i2 

3535 

3557 

358o 

36o3 

3625 

I 

58 

i5og 

i53 

i553 

i575  i597 

1619 

59 

3648 

367o 

3693 

37i6 

3738 

376i 

O 

59 

1640 

1662 

1  684 

I706;I728 

i749  o 

60" 

50" 

40" 

30" 

20" 

10" 

d 

60" 

50" 

40" 

30"   20"   10" 

d 

Co-sine  of  47 

Degrees. 

g 

Co-sine  of  46  Degrees. 

1 

PPartJ1"  2"  3"  4// 

5"  6"  7"  8"  9" 

.  f  1"  2"  3"  4"  5"  6"  7"  9"  9" 

F>lart{  2579 

11  14  16  18  21 

in\  2   4   7   9  11  13  16  18  20 

LOGARITHMIC    TANGENTS. 


1 

Tangent  of  42  Degrees. 

a 

Tangent  of  43  Degrees. 

s 

0" 

10" 

20"  1  30" 

40" 

50" 

§ 

0"     10"   20" 

30" 

40" 

50" 

o 

9.954437 

448o 

4522 

4564 

4607 

4649 

59 

0 

9.969656 

9698 

974o 

9783 

9825 

9867 

59 

I 

469i 

4734 

4776 

4819 

486  1 

49o3 

58 

I 

99°9 

995i 

9994 

..36 

..78 

.  120 

58 

2 

4g46 

4988 

5o3o 

5o73 

5n5 

5r57 

57 

2 

9.97oi62 

O205 

0247 

0289 

o33i 

o373 

57 

3 

5200 

5242 

5284 

5327 

5369 

54n 

56 

3 

o4i6 

o458 

o5oo 

o542 

o584 

0627 

56 

4 

5454 

5496 

5538 

558i 

5623 

5665 

55 

4 

o669 

0711 

o753 

0796 

o838 

0880 

55 

5 

57o8 

575o 

5792 

5835 

5877 

59r9 

54 

5 

O922 

o964 

1007 

1049 

1091 

n33 

54 

6 

596i 

6oo4 

6o46 

6088 

6i3i 

6i73 

53 

6 

n75 

1218 

1260 

1302 

1  344 

i386 

53 

7 

62i5 

6258 

63oo 

6342 

6385 

6427 

52 

7 

1429 

1471 

i5i3 

i555 

i597 

i64o 

52 

8 

6469 

65i2 

6554 

6596 

6639 

6681 

5i 

8 

1682 

1724 

1766 

1808 

i85i 

i893 

5i 

9 

6723 

6766 

6808 

685o 

6893 

6935 

5o 

9 

i935 

i977 

20I9 

2062 

2104 

2l46 

*)0 

10 

9.956977 

7020 

7062 

7104 

7i46 

7:89 

49 

10 

9.972188 

2230 

2273 

23i5 

2357 

2399 

49 

ii 

7231 

7273 

73i6 

7358 

7400 

7443 

48 

ii 

244i 

2484 

2526 

2568 

2610 

2652 

48 

12 

7485 

7527 

757o 

7612 

7654 

7697 

47 

12 

2695 

2737 

2779 

2821 

2863 

29o5 

47 

i3 

7739 

7781 

7823 

7866 

79o8 

795o 

46 

i3 

2948 

2990 

3o32 

3o74 

3n6 

3i59 

46 

i4 

7993 

8o35 

8077 

8120 

8x62 

8204 

45 

i4 

3201 

3243 

3285 

3327 

337o 

34l2 

45 

i5 

8247 

8289 

833i 

8373 

84i6 

8458 

44 

i5 

3454 

3496 

3538 

358i 

3623 

3665 

44 

16 

85oo 

8543 

8585 

8627 

8670 

8712 

43 

16 

37o7 

3749 

379i 

3834 

3876 

39i8 

43 

i? 

8754 

8796 

8839 

8881 

8923 

8966 

42 

I7 

3960 

4O02 

4o45 

4o87 

4129 

4171 

42 

18 

9008 

goSo 

9093 

9i35 

9i77 

92I9 

4i 

18 

42  I  3 

4255 

4298 

434o 

4382 

4424 

4i 

J9 

9262 

93o4 

9346 

9389 

943i 

9473 

4o 

J9 

4466 

45o9 

455i 

4593 

4635 

4677 

4o 

20 

9.959516 

9558 

96oo 

9642 

9685 

9727 

39 

20 

9.974720 

4762 

48o4 

4846 

4888 

493o 

39 

21 

9769 

9812 

9854 

9896 

9938 

998! 

38 

21 

4973 

5oi5 

5o57 

5099 

5i4i 

5i83 

38 

22 

9.960023 

oo65 

0108 

oi5o 

OI92 

0234 

37 

22 

5226 

5268 

53io 

5352 

5394 

5437 

37 

23 

0277 

0319 

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o4o4 

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36 

23 

5479 

552i 

5563 

56o5 

5647 

569o 

36 

24 

o53o 

0573 

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0667 

0700 

0742 

35 

24 

5732 

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58i6 

5858 

59oi 

5943 

35 

25 

0784 

0826 

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o953 

o996 

34 

25 

5985 

6027 

6o69 

6m 

6i54 

6i96 

34 

26 

io38 

1080 

1122 

n65 

1207 

i249 

33 

26 

6238 

6280 

6322 

6364 

64o7 

6449 

33 

27 

1292 

i334 

i376 

i4i8 

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i5o3 

32 

27 

6491 

6533 

6575 

6617 

6660 

6702 

32 

28 

1  545 

i587 

i63o 

1672 

1714 

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3i 

28 

6744 

6786 

6828 

6870 

69i3 

6955 

3i 

29 

1799 

i84i 

i883 

I926 

I968 

2010 

3o 

29 

6997 

7°39 

7081 

7123 

7i66 

7208 

3o 

3o 

9.962062 

2095 

2137 

2I79 

2222 

2264 

29 

3o 

9>97725o 

7292 

7334 

7377 

74i9 

746  1 

29 

3i 

23o6 

2348 

239I 

2433 

2475 

2517 

28 

3i 

75o3 

7545 

7587 

763o 

7672 

7714 

28 

32 

256o 

2602 

2644 

2686 

2729 

2771 

27 

32 

7756 

7798 

7840 

7882 

7925 

7967 

27 

33 

28i3 

2856 

2898 

2940 

2982 

3o25 

26 

33 

8oo9 

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8o93 

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8178 

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26 

34 

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3109 

3i5i 

3i94 

3236 

327a 

25 

34 

8262 

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8473 

25  • 

35 

3320 

3363 

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3447 

3489 

3532 

24 

35 

85i5 

8557 

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864i 

8684 

8726 

24 

36 

3574 

36i6 

3659 

3701 

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23 

36 

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8894 

8937 

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23 

37 

3828 

3870 

39I2 

3954 

3997 

4o39 

22 

37 

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9063 

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9i47 

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9232 

22 

38 
39 

4o8i 
4335 

4l23 

4377 

4i66 

44i9 

4208 
446  1 

4260 
45o4 

4292 

4546 

21 
20 

38 
39 

0274 
9527 

93i6 
9569 

9358 
9611 

94oo 
9653 

9442 
9695 

9485 
9738 

21 
2O 

4o 

9.964588 

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47i5 

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9.97978o 

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19 

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4842 

4884 

4926 

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5o53 

18 

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9.980033 

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18 

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5222 

5264 

53o6 

17 

42 

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o37o 

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ll 

43 

5349 

539i 

5433 

5475 

55i8 

556o 

16 

43 

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0623 

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0749 

16 

44 

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5687 

5729 

577i 

58i3 

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44 

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45 

5855 

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594o 

5982 

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6067 

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45 

1044 

1086 

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1255 

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46 

6109 

6i5i 

6i93 

6236 

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6320 

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1297 

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12 

47 

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1634 

1677 

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12 

48 

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48 

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1887 

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49 

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6911 

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49 

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10 

5o 

9.967123 

7i65 

7207 

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729i 

7334 

9 

5o 

9.982309 

235i 

2393 

2435 

2477 

25l9 

9 

5i 

7376 

74i8 

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75o3 

7545 

7587 

8 

5i 

2562 

2604 

2646 

2688 

2730 

2772 

8 

52 

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7672 

77i4 

7756 

7798 

784o 

7 

52 

2814 

2857 

2899 

294i 

2983 

3o25 

7 

53 

7883 

7925 

7967 

8oo9 

8o52 

8o94 

6 

53 

3067 

3io9 

3i52 

3i94 

3236 

3278 

6 

54 

8i36 

8178 

8220 

8263 

83o5 

8347 

5 

54 

3320 

3362 

34o4 

3447 

3489 

353i 

5 

55 

•  8389 

8432 

84?4 

85i6 

8558 

8600 

4 

55 

3573 

36i5 

3657 

3699 

374z 

3784 

4 

56 

8643 

8685 

8727 

8769 

8812 

8854 

3 

56 

3826 

3868 

3910 

3952 

3994 

4o37 

3 

57 

8896 

8938 

8980 

9023 

9o65 

9io7 

2 

57 

4079 

4l2I 

4x63 

42o5 

4247 

4289 

a 

58 

9149 

9192 

9234 

9276 

93i8 

936o 

I 

58 

4332 

4374 

44i6 

4458 

45oo 

4542 

i 

59 

94o3 

9445 

9487 

9529 

957i 

96i4 

O 

59 

4584 

4627 

4669 

4711 

4753 

4795 

o 

60" 

50" 

40" 

30" 

20" 

10" 

a 

60" 

50" 

40" 

30" 

20" 

10" 

. 

Co-tangent  of  47  Degrees. 

1 

Co-tangent  of  46  Degrees. 

1 

P  Part  5  l"  2"  3//  4"  5"  6"  7"  8"  9" 

PPoff1"  2"  3"  4"  5"  6"  7"  8"  9" 

£  4   8  13  17  21  25  30  34  38 

m\  4   8  13  17  21  25  30  34  38 

68 


LOGARITHMIC    SINES. 


jj 

Sine  of  44  Degrees. 

.3 

Sine  of  45  Degrees. 

i 

0" 

10" 

20"   30"   40" 

50" 

Si 

0" 

10" 

20" 

30" 

40" 

50" 

0 

9.  841771 

i793 

i8i5ii837  i858 

1880 

59 

09.849485 

95o6 

9527 

954* 

9569 

959o 

59 

I 

I902 

I924 

i946  i967  i989 

2OII 

58 

i 

96n 

9632 

9653 

9674 

9695 

97i6 

58 

2 

2o33 

2o55 

2O76 

2098  2I2O 

2l42 

5? 

2 

9738 

9759 

978o 

98oi 

9822 

9843 

57 

r. 

2i63 

2i85 

2207 

2229  225o 

2272  56 

*H 

9864 

9885 

99°6 

9927 

9948 

9969 

56 

4 

2294 

23i6 

2337 

2359238l 

24o3|55 

4 

999° 

.  .11 

..32 

..53 

..74 

..95 

55 

i 

242^ 

2446 

2468 

2490  25ll 

253354 

e 

9.85oi  16 

oi37 

oi58 

oi79 

O200 

O22I 

54 

6 

2555 

2577 

2598'262o  2642 

2663 

53 

6 

0242 

0263 

0284 

o3o5 

o326 

o347 

53 

\ 

2685 

2707 

2729  275o  2772 

27^ 

52 

7 

o368 

o388 

o4o9 

o43o 

o45i 

0472 

52 

28i5 

2837 

2859J288o  29O2 

5i 

8 

0493 

o5i4 

o535 

o556 

o577 

o598 

5i 

9 

2946 

2967 

29893on 

3o32 

3o54 

5o 

9 

06  1  9 

o64o 

0661 

0682 

0703 

0724 

5o 

10 

9.  843o76 

3097 

3n9{3i4i 

3i62 

3i84 

49 

10 

9.85o745 

o766 

0787 

o8o7 

0828 

o849 

49 

ii 

3206 

3227  3249  3271 

3292 

33i4 

48 

ii 

0870 

o89i 

O9I2 

o933 

o954 

o975 

48 

12 

3336 

3357 

3379  34oi 

3422 

3444 

47 

12 

o996 

IOI7 

io38 

io58 

io79 

IIOO 

47 

i3 

3466 

3487l35o9 

353o 

3552 

3574 

46 

i3 

II2I 

1  14- 

n63 

1184 

I2O5 

1226 

46 

i4 

3595 

36i7 

3639 

366o 

3682 

37o3 

45 

i4 

1246 

126-7 

1288 

i3o9 

i33o 

i35i 

45 

i5 

3725 

3747  3768 

379o 

38n 

3833 

44 

i5 

1372 

i393 

i4i3 

i434 

i455 

i476 

44 

16 

3855 

3876 

3898 

39i9 

394i 

3963 

43 

16 

i497 

i5i8 

i539 

i559 

i58o 

1601 

43 

17 

3984 

4oo6  4o27 

4o49 

4071 

4o92 

42 

17 

1622 

1  643 

1  664 

i685 

1705 

I726 

42 

18 

4n4 

4i354i57 

4178 

4200 

4222 

4i 

18 

1747 

i768 

i789 

1810 

i83o 

1861 

4i 

'9 

20 

4243 
9.  844372 

4265428643o8 
4394  44i64437 

4329 
4459 

435i 
448o 

4o 
39 

J9 
20 

1872 
9.85i997 

i893 
2018 

2o39 

i935 
2o59 

i955 
2080 

i976 

2IOI 

4o 
39 

21 

45o2 

452345454566 

4588 

46o9 

38 

21 

2122 

2i43 

2i63 

2184 

22O5 

2226 

38 

22 

463i 

4652  4674!4696 

4717 

4739 

37 

22 

2247 

2267 

2288 

23o9 

233o 

235o 

37 

23 

4760 

4782 

48o3 

4825 

4846 

4868 

36 

23 

2371 

2392 

c4i3 

2434 

2454 

2475 

36 

24 

4889 

49n 

4932 

4954 

4975 

4997 

35 

24 

2496 

25l7 

2537 

2558 

2579 

2600 

35 

25 

5oi8 

5o4o  5o6i 

5o83 

5io4 

5i26 

34 

25 

2620 

2641 

2662 

2683 

27o3 

2724 

34 

.  26 

5i47 

5i68  5i9o 

5211 

5233 

5254 

33 

26 

2745 

2766 

2786 

28o7 

2828 

2849 

33 

27 

5276 

529753i9 

534o 

5362 

5383 

32 

27 

2869 

2890 

291J 

293i 

2952 

2973 

32 

28 

54o5 

5426  5447  5469 

549o 

55i2 

3i 

28 

2994 

3oi4 

3o35 

3o56 

3o76 

3o97 

3i 

29 

5533 

5555 

55765598 

56i9 

564o 

3o 

29 

3n8 

3i39 

3i59 

3i8o 

3201 

3221 

3o 

3o 

9.  845662 

5683 

57055726 

5747 

5769 

29 

So 

9.  853242 

3263 

3283 

33o4 

3325 

3345 

29 

3i 

579° 

58i2 

58335855 

5876  5897 

28 

3i 

3366 

3387 

34o8 

3428 

3449 

347o 

28 

32 

59i9 

594o  5962 

5983 

6oo4  6026 

27 

32 

349o 

35n 

3532 

3552 

3573 

3594 

27 

33 

6047 

6o69  6o9o 

6m 

6i336i54 

26 

33 

36i4 

3635 

3655 

3676 

3697 

37i7 

26 

34 

6i75 

6197 

6218 

6240 

6261 

6282 

25 

34 

3738 

3759 

3779 

38oo 

382i 

384i 

25 

35 

63o4 

6325 

6346 

6368 

638964io 

24 

35 

3862 

3883 

39o3 

3924 

3944 

3965 

24 

36 

6432 

6453  64?4 

6496 

65i76539 

23 

36 

3986 

4oo6 

4027 

4o47 

4o68 

4o89 

23 

37 

656o 

658i 

66o3 

6624 

66456667 

22 

37 

4io9 

4i3o 

4i5i 

4171 

4l92 

4212 

22 

38 

6688 

67o9  673i 

67^267736794 

21 

38 

4233 

4254 

4274 

4295 

43i54336 

21 

39 

6816 

68376858 

6880 

69oi  6922 

2O 

39 

4356 

4377 

4398 

44i8 

44394450 

2O 

4o 

9.846944 

6965  6986 

7008 

•jO29  7o5o 

19 

4o 

9.  85448o 

45oo 

452i 

4542 

4562 

4583 

19 

4i 

7071 

7o93 

7114 

7i35 

71577178 

18 

4i 

46o3 

4624 

4644 

4665 

4686 

4706 

18 

42 

7i99 

7220  7242 

7263 

7284^305 

17 

42 

4727 

4747 

4768 

4788 

48r>9 

4829 

17 

43 

7348  7369 

739i 

74i27433 

16 

43 

485o 

4870 

489i 

49n 

4932 

4953 

16 

44 

7454 

7476  7497 

75i8 

7539  7561 

i5 

44 

4973 

4994 

5oi4 

5o35 

5o55 

5o76 

i5 

45 

7582 

7603  7624 

7645 

7667  7688 

i4 

45 

5o96 

5n7 

5i37 

5i58 

5i78 

5i99 

i4 

46 

77°9 

77307752 

7773 

779478i5 

i3 

46 

52I9 

524o 

5260 

5281 

53oi 

5322 

i3 

47 

7836 

7858  7879 

79oo 

792ij7943 

12 

47 

.5342 

5363 

5383 

54o4 

5424 

5445 

12 

48 

7964 

7985]8oo6 

8027 

8o49  8070 

II 

48 

5465 

5485 

55o6 

5526 

5547 

5567 

II 

49 

8o9i 

8112 

8i33 

8i54 

81768^7 

10 

49 

5588 

56o8 

5629 

5649 

567o 

569o 

IO 

5o 

9.  848218 

8239  8260 

8282 

83o38324 

9 

5o 

9.8557n 

573i 

575i 

5772 

5792 

58i3 

9 

5i 

8345 

8366  8387 

84o9 

843o845i 

8 

5i 

5833 

5854 

5874 

5895 

59i5 

5935 

8 

52 

8472 

8493 

85i4 

8535 

85578578 

7 

52 

5956 

5976 

5997 

6017 

6o38 

6o58 

7 

53 

8599 

86208641 

8662 

8683  87o5 

6 

53 

6o78 

6o99 

6n9 

6i4o 

6160 

6180 

6 

54 

8726 

8747'8768 

8789 

8810  883i 

5 

54 

6201 

6221 

6242  6262 

6282  63o3 

5 

55 

8852 

8874 

8895 

89i6 

89378958 

4 

55 

6323634463646384 

64o5  6425 

4 

56 

8979 

9000  9O2I 

9o42 

9o63  9o85 

3 

56 

6446 

6466  6486  6507  6527  6547 

3 

57 

9io6 

9I27 

9i48  9i69 

9I90  92II 

2 

57 

6568 

6588 

66o9  66s9  6649  6670 

2 

58 

9232 

9253 

92749295 

93i6'9338 

I 

58 

669o  67io 

673i675i:677i  6792  i 

59 

9359 

938o 

94oi 

9422 

94439464 

O 

59 

6812  6832  6853  6873|689369i4  o 

60" 

50"  | 

40"   30" 

20"   10" 

j 

60"    |  50"   40"  i  30"  i  20"   10"   _. 

Co-sine  of  45  Degrees. 

1 

Co-sine  of  44  Degrees.     s 

t  •tn  o"  *V' 
P  Part  I 

4"  5"  6"  7"  8"  9" 

p  P  ,51"  2"  3"  4"  5"  6"  7"  8"  9"  : 

•"{  2   4   6 

9  11  13  15  17  19 

m\  2  4   6   8  10  12  14  17  19 

LOGARITHMIC    TANGENTS. 


1 

Tangent  of  44  Degrees. 

a 

Tangent  of  45  Degrees. 

jg 

0" 

10" 

20" 

30" 

40"  j  50" 

* 

0" 

10" 

20" 

30" 

40" 

50" 

o 

9.98483-7 

4879 

492I 

4964 

5oo6 

5o48 

59 

o 

IO.OOOOOO 

OO42 

oo84 

0126 

0168 

O2II 

59 

i 

5090 

5i32 

5i74 

52i6 

5259 

53oi 

58 

I 

0253 

0295 

o337 

o379 

O42I 

o463 

58 

2 

5343 

5385 

542-7 

5469 

55n 

5553 

57 

2 

o5o5 

o547 

o59o 

o632 

o674 

o7i6 

57 

3 

5596 

5638 

568o 

5722 

5764 

58o6 

56 

3 

o758 

0800 

0842 

0884 

0926 

o969 

56 

4 

5848 

5891 

5933 

5975 

6oi7 

6o59 

55 

4 

IOII 

io53 

io95 

n37 

"79 

1221 

55 

5 

6101 

6i43 

6i85 

6228 

6270 

63i2 

34 

5 

1263 

i3o5 

1  348 

1390 

1432 

i474 

54 

6 

6354 

6396 

6438 

648o 

6523 

6565 

53 

6 

i5i6 

i558 

1600 

1642 

1  684 

1727 

53 

7 

66o7 

6649 

669i 

6733 

6775 

68i7 

52 

7 

i769 

1811 

i853 

i895 

i937 

i979 

52 

8 

6860 

6902 

6944 

6986 

-7028 

7o7o 

5i 

8 

2O2I 

2o63 

2106 

2148 

2190 

2232 

5i 

9 

7II2 

7i54 

7i97 

7s39 

-7281 

7323 

5o 

9 

2274 

23i6 

2358 

2400 

2442 

2485 

5o 

10 

9.987365 

74o7 

7449 

749  1 

7534 

7576 

49 

10 

IO.OO2527 

2569 

2611 

2653 

2695 

2737 

49 

ii 

-7618 

766o 

7702 

7744 

7786 

7829 

48 

ii 

2779 

2821 

2864 

2906 

2948 

299° 

48 

12 

7871 

79i3 

7955 

7997 

8o39 

8081 

47 

12 

3o32 

3o74 

3n6 

3i58 

3200 

3243 

47 

i3 

8i23 

8166 

8208 

825o 

8292 

8334 

46 

i3 

3285 

3327 

3369 

34n 

3453 

3495 

46 

i4 

8376 

84i8 

846o 

85o3 

8545 

8587 

45 

i4 

3537 

3579 

3622 

3664 

37o6 

3748 

45 

!5 

8629 

867i 

87i3 

8755 

8797 

884o 

44 

i5 

379° 

3832 

3874 

3916 

3958 

4ooi 

44 

16 

8882 

8924 

8966 

9008 

9o5o 

9092 

43 

16 

4o43 

4o85 

4l27 

4i69 

4211 

4253 

43 

ll 

9i34 

9i77 

9219 

9261 

93o3 

9345 

42 

I7 

4295 

4337 

438o 

4422 

4464 

45o6 

42 

18 

9387 

9429 

9471 

95i3 

9556 

9598 

4i 

18 

4548 

459o 

4632 

4674 

47i6 

4759 

4i 

19 

964o 

9682 

9724 

9766 

9808 

985o 

4o 

19 

48oi 

4843 

4885 

4927 

4969 

Son 

4o 

20 

9.989893 

9935 

9977 

..61 

.io3 

39 

20 

io.oo5o53 

5o95 

5i38 

5i8o 

5222 

5264 

39 

21 

9.99oi45 

oi87 

0230 

O272 

o3i4 

o356 

38 

21 

53o6 

5348 

539o 

5432 

5474 

55i7 

38 

22 

o398 

o44o 

0482 

0524 

o567 

0609 

37 

22 

5559 

56oi 

5643 

5685 

5727 

5769 

37 

23 

o65i 

0693 

o735 

°777 

0819 

0861 

36 

23 

58!  i 

5854 

5896 

5938 

5980 

6022 

36 

24 

o9o3 

0946 

0988 

io3o 

IO72 

ni4 

35 

24 

6o64 

6106 

6i48 

6i9o 

6233 

6275 

35 

25 

n56 

1198 

1240 

1283 

i325 

i367 

34 

25 

63i7 

6359 

64oi 

6443 

6485 

6527 

34 

26 

i4o9 

i45i 

1493 

i535 

1-577 

1620 

33 

26 

6569 

6612 

6654 

6696 

6738 

678o 

33 

27 

1662 

i7o4 

i746 

i788 

i83o 

l872 

32 

27 

6822 

6864 

6906 

6949 

6991 

7o33 

32- 

28 

i9i4 

1956 

1999 

2o4l 

2o83 

2125 

3i 

28 

7o75 

7117 

7l59 

720I 

7243 

7285 

3i 

29 

2l67 

2209 

r 

225l 

2293 

2336 

2378 

3o 

29 

7328 

737o 

74i2 

7454 

7496 

7538 

3o 

3o 

9.992420 

2462 

2504 

2546 

2588 

263o 

29 

3o 

io.oo758o 

-7622 

7664 

77°7 

7749 

7791 

29 

3i 

2672 

27l5 

2757 

2799 

2841 

2883 

28 

3i 

7833 

7875 

79i7 

7959 

8001 

8o44 

28 

32 

2925 

296? 

3009 

3o5i 

3o94 

3i36 

27 

32 

8086 

8128 

81-70 

8212 

8254 

8296 

27 

33 

3i78 

3220 

3262 

33o4 

3346 

3388 

26 

33 

8338 

838o 

8423 

8465 

85o7 

8549 

26 

34 

343i 

3473 

35i5 

3557 

3599 

364i 

25 

34 

859i 

8633 

8675 

87i7 

876o 

8802 

25 

35 

3683 

3725 

3767 

38io 

3852 

3894 

24 

35 

8844 

8886 

8928 

8g7o 

9012 

9o54 

24 

36 

3936 

3978 

4020 

4062 

4io4 

4i46 

23 

36 

9°97 

9i39 

9181 

9223 

9265 

93o7 

23 

37 

4189 

423i 

4273 

43i5 

4357 

4399 

22 

37 

9349 

939i 

9433 

9476 

95i« 

956o 

22 

38 

444i 

4483 

4526 

4568 

46io 

4652 

21 

38 

96O2 

9644 

9686 

9?28 

977o98!3 

21 

39 

4694 

4736 

4778 

4820 

4862 

4905 

2O 

39 

9855 

9897 

9939 

998i 

..23 

..65 

2O 

4o 

9-994947 

4989 

5o3i 

5o73 

5n5 

5i57 

I9 

4o 

IO.OIOI07 

oi5o 

0192 

0234 

0276 

o3i8 

'9 

4i 

5199 

5284 

5326 

5368 

54io 

18 

4i 

o36o 

0402 

o444 

o487 

o529 

o57i 

18 

42 

5452 

5494 

5536 

5578 

5620 

5663 

!7 

42 

o6i3 

o655 

o697 

o739 

0-781 

0823 

17 

43 

57o5 

5747 

5789 

583i 

5873 

59i5 

16 

43 

0866 

0908 

o95o 

0992 

io34 

io76 

16 

44 

5957 

5999 

6o42 

6o84 

6126 

6168 

i5 

44 

1118 

1  1  60 

1203 

1245 

I287 

i329 

i5 

45 

6210 

6252 

6294 

6336 

6378 

6421 

i4 

45 

i37i 

i4i3 

i455 

i497 

i54o 

i582 

i4 

46 

6463 

65o5 

6547 

6589 

663i 

6673 

i3 

46 

1624 

1666 

I7o8 

i75o 

I792 

i834 

18 

47 

67i5 

6757 

6800 

6842 

6884 

6926 

12 

47 

i877 

1919 

i96i 

2O03 

2045 

208-7 

12 

48 

6968 

7010 

7o52 

7o94 

7i36 

7i79 

II 

48 

2I29 

2I7I 

22l4 

2256 

2298J234o 

II 

49 

•7221 

7263 

73o5 

7347 

7389 

743i 

10 

49 

2382 

2424 

2466 

25o9 

255i  2593 

IO 

5o 

9.997473 

75!5 

7558 

76oo 

7642 

7684 

9 

5o 

10.012635 

2677 

2719 

276l 

28o3  2846 

9 

5i 

7726 

7768 

78io 

7852 

789417937 

8 

5i 

2888 

2930 

2972 

3oi4 

3o56 

3o98 

8 

52 

7979 

8021 

8o63 

8io5 

8i47|8i89 

7 

52 

3i4o 

3i83 

3225 

3267 

33o9 

335i 

7 

53 

823i 

8273 

83i6 

8358 

84oo 

8442 

6 

53 

3393 

3435 

3477 

3520 

3562  36o4 

6 

54 

8484 

8526 

8568 

8610 

8652 

8695 

5 

54 

3646 

3688 

373o 

3772 

38i5 

3857 

5 

55 

8737 

8779 

8821 

8863 

89o5 

8947 

4 

55 

3899 

3g4i 

3983 

4o25 

4o67 

4109 

4 

56 

57 

8989  9031 
9242  928^ 

90-74 
9326 

9n6 
9368 

9i58 
94io 

9200 
9453 

3 

2 

56 

4i52 
44o4 

4i94 

4447 

4236 
4489 

4278 

453i 

4320 
4573 

4362 
46i5 

3 

2 

58 

9495 

95379579 

962I 

9663 

97o5 

I 

58 

4657 

4699 

474i 

4?84 

4826 

4868 

I 

59 

9747 

97899832 

9874 

99i6 

9958 

0 

59 

49io 

4952 

4994 

5o36 

5o79j5i2i 

0 

60"      50"   40" 

30" 

20"   10" 

. 

60"      50" 

40" 

30" 

20"  |  10" 

- 

Co-tangent  of  45  Degrees. 

s  . 

Co-tangent  of  44  Degrees. 

s 

A  1"  2"  3"  4"  5"  6"  7"  8"  9" 

p  p   (  1"  2"  3"  4"  5"  6"  7"  8"  9" 

.rartj  4  8  13  17  21  25  29  34  38 

P.Part^  4   g  13  17  21  25  29  34  38 

70 


LOGARITHMIC    SINES. 


d 

Sine  of  46  Degrees. 

d 

Sine  of  47  Degrees. 

ii 

0"    |  10"  |  20" 

i  -30" 

40"   50" 

0"    |  10"   20"  [  30" 

50" 

0^9.  866934  6964  6976 

,6995 

7016  7036  69 

09.86412-7 

4i47  4167  4186,4206 

4226 

69 

i 

7066  7076  7097 

7117 

71377168  58 

i 

4245 

42664284 

43o4!4324 

4343 

58 

2 

7178 

7i98 

7219 

7239 

7269 

727967 

2 

4363 

4383  4402 

4422;444i 

446  1 

57 

3 

4 

73oo 

7422 

7320 

7442 

7340  7361 
7462  7482 

738i  74oi  56 
7603762355 

3 

4 

448  1 
4598 

45oo 

46i8 

4620 
4637 

4539!4559 
46574676 

4579 
4696 

56 
55 

5 

7543  7563 

7584 

7604 

7624  7645  54 

5 

4716 

4735 

4755 

4774 

4794 

48i3 

54 

6 

7665J7685 

7706 

7726 

7746  7766  53 

6 

4833 

4853 

4872 

4892 

4911 

493i 

53 

7 

8 

7786 
7908 

7807 

7928 

7827 
7948 

7847 
7968 

7867 
7989 

7888 
8009 

62 
5i 

8 

4960 
5o68 

49704990 
5o87j5io7 

6009 
6126 

6029 

5i46 

5o48 
6166 

62 
5i 

9 

8029 

8o49  8070  8o9o 

8no;8i3o  5o 

9 

5i85 

6204 

6224 

6244 

5263 

5283 

5o 

10 

9.868161 

8171 

8191 

8211 

823i  82'52 

49 

10 

9-865302 

5322 

534i 

536i 

538o 

54oo 

49 

ii 

8272 

8292 

83i2 

8332 

8353  8373 

48 

ii 

5419 

5439 

5458 

5478 

5497 

55i7 

48 

12 

8393 

84i3 

8433  8454 

8474 

8494 

47 

12 

5536 

5556  5575 

5595 

56i4 

5634 

47 

i3 

85i4 

8534 

8554 

8676 

86968616 

46 

i3 

5653 

5673 

6692 

6712 

573i 

575i 

46 

i4 

8635 

8655 

8676 

8696 

87i6:8736 

45 

i4 

6770 

6790 

6809 

6828 

5848 

5867 

45 

16 

8766 

8776 

87968817 

88378867 

44 

16 

6887 

6906 

6926 

5945 

6966 

5984 

44 

16 

8877 

8897 

8917 

8937 

89688978 

43 

16 

6oo4 

6023 

6042 

6062 

6081 

6101 

43 

17 

8998 

9oi8 

9o38  9068 

9078:9098 

42 

17 

6120 

6.i4o 

6169 

6179 

6198 

6217 

42 

18 

9119 

9i39 

91699179 

91999219 

4i 

18 

6237 

6266 

6276 

6296 

63i5 

6334 

4i 

19 

9239 

9269 

9279  gSoo 

9320^340 

4o 

'9 

6353 

6373 

6392 

6412 

643i 

645o 

4o 

20  o.o5o3oo 

938o 

QdOO 

9420 

944o  9460 

39 

20 

9.866470 

6489 

65o9 

6628 

6547 

6667 

39 

21 

948o 

9601 

9621 

9641 

9661  9681 

38 

21 

,6586 

6606 

6626 

6644 

6664 

6683 

38 

22      9601 

9621 

9641 

9661 

9681  9701 

37 

22 

6703 

6722 

674i 

6761 

6780 

6800 

37 

23    9721 

9741 

976i 

9.781  98o2  9822 

36 

23 

6819 

6838 

6858 

6877 

6896 

6916 

36 

24    9842 

9862 

9882 

9902 

9922  9942 

35 

24 

6935 

6954 

6974 

6993 

7013 

7032 

35 

26    9962 

9982 

.  .  .2 

.  .22 

.  .42).  .62 

34 

25 

7061 

7071 

709o 

7109 

7129 

7148 

34 

26  9.860082 

OI02 

0122 

0142 

0162  0182 

33 

26 

7167 

7187 

7206 

7226 

7245 

7264 

33 

27!     O2O2 

0222 

O242  O262 

0282  o3o2 

32 

27 

7283 

73o3 

7322 

7341 

736i 

738o 

32 

28      0322 

0342 

o362  o382 

o4o2  o422 

3i 

28 

7399 

7419 

7438 

7457 

7476 

7496 

3  1 

29      O442 

0462 

0482  0602 

O522:o542 

3o 

29 

-7616 

7534 

7554 

7573 

•7692 

7612 

3o 

309.860662 

0582 

0602  0622  0642  0662 

29 

3o 

9-86763i 

7660 

7660. 

7689 

77o8 

7727 

29 

3i 

0682 

O7O2 

0722  0742 

0762  0782 

28 

3i 

7747 

7766 

7785 

780/1 

7824 

7843 

28 

32 

0802 

0822 

0842  0862 

0882  0902 

27 

32 

7862 

7882 

79oi 

7920 

7939 

•7969 

27 

33 

O922 

094l 

0961 

098l 

1001 

1  02  1 

26 

33 

797s 

7997 

8016 

8o36 

8o55 

8074(26 

34 

io4i 

1061 

1081 

IIOI.II2I 

n4i 

26 

34 

8o93 

8ii3 

8i32 

8161 

8i7o 

8190  26 

35 

1161 

1181 

1201 

1221  I24O 

1260 

24 

35 

8209 

8228 

8247 

8267 

8286 

83o5 

24 

36 

1280 

i3oo 

l320 

i34o 

i36o 

i38o 

23 

36 

8324 

8343 

8363 

8382 

84oi 

8420 

23 

37 

i4bo 

l420 

i439 

1469  1479 

1499 

22 

37 

844o 

8459 

8478 

8497 

8616 

8536 

22 

38 

1619 

i539 

i559 

1679  159911618 

21 

38 

8555 

8574 

8593 

8612 

8632 

865  1 

21 

39 

i638 

1668 

1678 

1698  1718 

1738 

20 

39 

867o 

8689 

8708 

8728 

8747 

8766 

20 

4o 

9.  86:768 

1777 

170.7 

1817  1837 

1867 

'9 

4o 

9.868785 

8804 

8823 

8843 

8862 

8881 

19 

4i 

1877 

1897 

1916 

1936  1966 

1976 

18 

4i 

8900 

8919 

8939 

8958 

8977 

8996 

1  8 

42 

i996 

2016 

2o35 

2066  2076 

2096 

I7 

42 

9016 

9o34 

9o53 

9o73 

9092 

9111 

17 

43 

21  16 

2i35 

2164 

2174  21  94 

22l4 

16 

43 

9i3o 

9149 

9i68 

9i88 

92°7 

9226 

16 

44 

2234 

2264 

2273 

2293  23i3 

2333 

i5 

44 

9246 

9264 

9283 

9302 

9321 

934i 

16 

45 

2353 

2372 

2392 

•J-ll  2  2432 

2462 

i4 

45 

936o 

9379 

9398 

94i79436 

9455 

r4 

46 

2471 

2491 

2611 

253i  2661 

2670 

i3 

46 

9474 

9494 

95i3 

9532955i 

957o 

i3 

47 

260.0 

2610 

263026602669 

2689 

12 

47 

9689 

9608 

9627 

9646  9665 

9685 

12 

48 

2709 

2729 

2748  2768  2788 

2808 

II 

48 

9704 

9723 

9742 

9761 

9780 

9799  IJ 

49 

2827 

2847 

2867  2887  2906 

2926 

IO 

49 

9818 

9837 

9866 

9876 

9894 

99x410 

5o 

9.  862946 

2966 

2986 

3oo5 

3o25 

3o45 

9 

5o 

9.869933 

9962 

9971 

9990 

...9 

..28  9 

61 

3o64 

3o84 

3io4  3i24 

3i43 

3i63 

8 

61 

9.87oo47 

0066  0086 

oio4 

8 

62 

3i83 

32o3 

3222 

3242 

3262 

3281 

7 

62 

f 
0161 

0180  0199 

0218  0238  0267 

7 

53 

33oi 

332i 

334i 

336o 

338o 

34oo 

6 

53 

O276 

0296 

o3i4 

o3'33 

o35-3  0371 

6 

54 

34i9 

3439 

3459 

3478 

3498 

35i8 

5 

54 

oSgo 

0409 

0428 

o447  o466  o485 

5 

55 

3538 

3557 

3577 

3597 

36i6 

3636 

4 

55 

o5o4 

0623  0642 

0661  0680 

0699 

4 

56 

3656 

3676 

3696 

37i5 

3734 

3754 

3 

56 

0618  o637  0666  o675  0694 

o7i3i  3 

57 

3774 

3793 

38i3 

3833 

3852 

3872 

2 

57 

o732  0761  0770  0789  0808 

0827   2 

58 

3892 

3911 

393i 

395i 

397o 

399o 

I 

58 

o846;o865o884'o9o3  0922  0941  i 

59 

4oio 

4029 

4049 

4069 

4o88 

4io8 

O 

69 

096009790998101710361064  ° 

60"     50" 

40"  |  30"   20" 

10" 

•  a 

60"    i  50"   40"   30"   20"   10"   ^ 

Co-sine  of  43 

Degrees. 

S 

Co-sine  of  42  Degrees. 

(  \n  2"  3"  4" 

5"  6"  7"  8"  9" 

„  p.  f(  1"  2"  3"  4"  5"  6"  7"  8"  9" 

P.  Part  J  2468 

10  12  14  16  18  [     "*\  2   4   6   8  10  12  14  15  17 

LOGARITHMIC    TANGENTS. 


71 


1 

Tangent  of  46  Degrees. 

.s 

Tangent  of  47  Degrees. 

s 

0" 

10" 

20" 

30" 

40" 

50" 

m 

0" 

10"|  20" 

30" 

40" 

50" 

o 

*o.oi5i63 

52o5 

5247 

5289 

533i 

5373 

59 

0 

io.o3o344 

o386 

0429 

0471 

o5i3 

o555 

59 

i 

54i6 

5458 

55oo 

5542 

5584 

5626 

58 

i 

oS97 

o64o 

0682 

O72<4 

o766 

0808 

58 

2 

5668 

571  1 

5753 

5795 

5837 

5879 

57 

2 

o85i 

o893 

0935 

°977 

IO20 

1062 

57 

3 

5921 

5963 

6006 

6o48 

6o9o 

6i32 

56 

3 

no4 

n46 

1188 

I23l 

I273 

i3i5 

56 

4 

6174 

6216 

6258 

63oi 

6343 

6385 

55 

4 

i357 

i4oo 

1  442 

i484 

i526 

1  568 

55 

5 

6427 

6469 

65n 

6553 

6596 

6638 

54 

5 

1611 

i653 

i695 

1737 

1780 

1822 

54 

6 

6680 

6722 

6764 

6806 

6848 

689i 

53 

6 

1864 

I9o6 

1948 

i99i 

2o33 

2075 

53 

7 

6933 

6975 

7017 

7o5'9 

7101 

7i43 

52 

7 

2117 

2160 

2202 

2244 

2286 

2328 

52 

8 

7186 

7228 

7270 

73l2 

7354 

7396 

5i 

8 

2371 

24l3 

2455 

2497 

254o 

2582 

5i 

9 

.  7438 

748  1 

7523 

7565 

7607 

7649 

5o 

9 

2624 

2666 

2709 

2751 

2793 

2835 

5o 

10 

10.017691 

7733 

7776 

78i8 

7860 

7902 

49 

10 

10.032877 

292O 

2962 

3oo4 

3o46 

3o89 

49 

ii 

7944 

7986 

8028 

8071 

8ii3 

8i55 

48 

ii 

3i3i 

3i73 

32i5 

3258 

33oo 

3342 

48 

12 

8197 

8239 

8281 

8323 

8366 

84o8 

47 

12 

3384 

3426 

3469 

35n 

3553 

3595 

47 

i3 

845o 

8492 

8534 

8576 

8618 

8661 

46 

i3 

3638 

368o 

3722 

3764 

38o7 

3849 

46 

i4 

87o3 

8745 

8787 

8829 

8871 

89i4 

45 

i4 

389i 

3933 

3976 

4oi8 

4o6o 

4lO2 

45 

i5 

8956 

8998 

9040 

9082 

9I24 

9i66 

44 

:5 

4i45 

4i87 

4229 

4271 

43i3 

4356 

44 

16 

9209 

9a5i 

9293 

9335 

937:7 

94i9 

43 

16 

4398 

444o 

4482 

4525 

4567 

46o9 

43 

*7 

9462 

95o4 

9546 

9588 

963o 

9672 

42 

17 

465  1 

4694 

4736 

4778 

4820 

4863 

42 

18 

97i4 

9757 

9799 

9841 

9883 

9925 

4i 

18 

49o5 

4947 

4989 

5o32 

5074 

5u6 

4i 

J9 

9967 

.  .  10 

.  .62 

•  •94 

.136 

.178 

4o 

X9 

5i58 

52OI 

5243 

5285 

5327 

5370 

4o 

20 

IO.O2O22O 

0262 

o3o5 

o347 

o389 

o43  1 

39 

20 

io.o354i2 

5454 

5496 

5539 

558i 

5623 

39 

21 

0473 

o5i5 

o558 

0600 

0642 

o684 

38 

21 

5665 

57o8 

5750 

5792 

5834 

5877 

38 

22 

0726 

0768 

0810 

o853 

o895 

o937 

37 

22 

59i9 

596i 

6oo3 

6o46 

6088 

6i3o 

37 

23 

0979 

1021 

io63 

1106 

1148 

1190 

36 

23 

6172 

62*6 

6257 

6299 

634i 

6384 

36 

24 

1232 

1274 

i3i6 

i359 

i4oi 

1  443 

35 

24 

6426 

6468 

65ii 

6553 

6595 

6637 

35 

25 

i485 

1527 

i569 

1612 

i654 

1696 

34 

25 

6680 

6722 

6764 

6806 

6849 

689i 

34 

26 

i738 

1780 

1822 

i865 

I907 

1949 

33 

26 

6933 

6975 

7018 

7060 

7102 

7i44 

33 

27 

1991 

2o33 

2075 

2118 

2160 

2202 

32 

27 

1  7187 

7229 

7271 

73i4 

7356 

7398 

32 

28 

2244 

2286 

2328 

237o 

24i3 

2455 

3i 

28 

744o 

7483 

7525 

7567 

76o9 

7652 

3i 

29 

2497 

2539 

258i 

2623 

2666 

27o8 

3o 

29 

7694 

7736 

7778 

7821 

7863 

79o5 

36 

3o 

10.022750 

2792 

2834 

2877 

29I9 

2961 

29 

3o 

io.o37948 

799° 

8o32 

8074 

8117 

8i59 

29 

3i 

3oo3 

3o45 

3o87 

3i3o 

3l72 

3214 

28 

3i 

8201 

8243 

8286 

8328 

837o 

84i3 

28 

32 

3256 

3298 

334o 

3383 

3425 

3467 

27 

32 

8455 

8497 

8539 

8582 

8624 

8666 

27 

33 

35o9 

355i 

3593 

3636 

3678 

3720 

20 

33 

8708 

875i 

8793 

8835 

8878 

892O 

26 

34 

3762 

38o4 

3846 

3889 

393i 

3973 

25 

34 

8962 

9oo4 

9o4? 

9o89 

9i3i 

9i74 

25 

35 

4oi5 

4o57 

4o99 

4142 

4i84 

4226 

24 

35 

9216 

9258 

93oo 

9343 

9385 

9427 

24 

36 

4268 

43io 

4353 

4395 

4437 

4479 

23 

36 

9470 

95l2 

9554 

9596 

9639 

968i 

23 

3? 

452i 

4563 

46o6 

4648 

469o 

4732 

22 

37 

9723 

9766 

98o8 

985o 

9892 

9935 

22 

38 

4774 

48i7 

4859 

4901 

4943 

4985 

21 

38 

9977 

.  .19 

..62 

.  104 

.i46 

.188 

21 

39 

5027 

6070 

5lI2 

5i54 

5i96 

5238 

20 

39 

io.o4o23i 

0273 

o3i5 

o358 

o4oo 

0442 

2O 

4o 

10.025280 

5323 

5365 

5407 

5449 

5491 

I9 

4o 

io.o4o484 

0527 

o569 

06  1  1 

o654 

o696 

I9 

4i 

5534 

5576 

56i8 

566o 

5702 

5745 

18 

4i 

o738 

0781 

0823 

o865 

o9o7 

o95o 

18 

42 

5787 

5829 

5871 

59i3 

5955 

5998 

«7 

42 

0992 

io34 

I077 

in9 

1161 

1204 

r7 

43 

6o4o 

6082 

6124 

6166 

6209 

625i 

1  6 

43 

1246 

1288 

i33o 

i373 

i4i5 

i457 

16 

44 

6293 

6335 

6377 

6419 

6462 

65o4 

i5 

44 

i5oo 

1  542 

1  584 

162-7 

i669 

1711 

i5 

45 

6546 

6588 

663o 

6673 

67i5 

6757 

i4 

45 

1753 

1796 

i833 

1880 

I923 

i965 

i4 

46 

6799 

684i 

6884 

6926 

6968 

7010 

i3 

46 

2007 

2o5o 

2092 

2134 

2177 

22I9 

i3 

4? 

7062 

7o95 

7i37 

7179 

722I 

7263 

12 

47 

2261 

23o3 

2346 

2388 

243o 

2473 

12 

48 

73o5 

7348 

739o 

7432 

7474 

75i6 

I  I 

48 

25i5 

2557 

2600 

2642 

2684 

2727 

II 

49 

7559 

7601 

7643 

7685 

7727 

777° 

10 

49 

2769 

2811 

2854 

2896 

2938 

298o 

10 

So 

10.027812 

7854 

7896 

7938 

7981 

8023 

0 

5o 

io.o43o23 

3o65 

3io7 

3i5o 

3i92 

3234 

9 

5  1 

8o65 

8107 

8i49 

8192 

8'234 

8276 

8 

5i 

3277 

33i9 

336i 

34o4 

3446 

3488 

8 

52 

83i8 

836o 

84o3 

8445 

8487 

8529 

7 

52 

353i 

3573 

36i5 

3658 

3700 

3742 

7 

S3 

8571 

86i4 

8656 

8698 

874o 

8782 

6 

53 

3785 

3827 

3869 

39I2 

3954 

3996 

6 

54 

8825 

8867 

8909 

895i 

8993 

9o36 

5 

54 

4o39 

4o8i 

4123 

4i65 

4208 

425o 

5 

55 

9078 

9120 

9162 

9204 

9247 

9289 

4 

55 

4292 

4335 

4377 

44i9 

4462 

45o4 

4 

56 

933i 

9373 

94i6 

9458 

gSoo 

9542 

3 

56 

4546 

4589 

463i 

4673 

4716 

4758 

3 

57 

9584 

9627 

9669 

97" 

9753 

9795 

2 

57 

48oo 

4843 

4885 

4927 

497o 

5oi2 

2 

58 

9838 

9880 

9922 

9964 

...6 

..49 

I 

58 

5o54 

5o97 

5i39 

5i8i 

5224 

5266 

I 

59 

io.o3oo9i 

oi33 

0175 

02  I  7 

0260 

0302 

0 

59 

53o9 

535i 

5393 

5436 

5478 

552o 

O 

60" 

50" 

40" 

30" 

20" 

10" 

jj 

60" 

50" 

40" 

30" 

20" 

10" 

a 

Co-tangent  of  43  Degrees. 

s 

Co-tangent  of  42  Degrees. 

i 

p  p   C  1"  2"  3"  4"  5"  6"  7"  8"  9" 

.(  1"  2"  3"  4"  5"  6"  7"  S"  9" 

(4   8  13  17  21  25  30  34  38 

~            •               i 

lrl\  4   8  13  17  21  25  30  34  38 

72 


LOGARITHMIC    SINES. 


.9 

Sine  of  48  Degrees. 

d 

Sine  of  49  Degrees. 

s 

0"     10" 

20"  |  30"  ;  40" 

50" 

9 

0-'     10" 

20"   30"  |  40" 

50" 

0 

9.87io73|io92 

IIII  Il3o  Il49 

1168 

59 

o 

9.  877780  7798 

-7816 

7835  7853 

787I 

39 

n87 

1206 

1225  1244  1263 

1282 

58 

I 

789o  79ofi 

7926 

7945  7963 

798i 

58 

2 

i3oi 

1320 

i339  i358  i377 

i395 

57 

2 

7999  8018 

8o36 

8o54:8o72 

8o9i 

57 

[ 

i4i4 

i433 

i452  i47i  i49o 

i5o9 

56 

'. 

8109  8127 

8i46 

81648182 

8200 

56 

L 

i528 
i64i 

i547 
1660 

i566  i585  1604 
i679  i698  1-71-7 

162255 

i73654 

L 
t 

8219 
8328 

8237|8255 
8346  8365 

8273J8292 

838384oi 

83io 
84i9 

55 
54 

6 

i755 

i774 

i793  i8n!i83o 

i849  53 

6 

8438 

8456 

8474 

8492851  1 

8529 

53 

7 

1868 

i887 

I9o6  1925  1944 

I962 

52 

7 

8547 

8565 

8583 

860218620 

8638 

52 

8 

1981 

2000  2019  2o38  2o57 

20-76 

5i 

8 

8656 

8675 

8693 

87n 

8729 

8747 

5i 

9 

2095 

2Il3 

2  I  32  2l5l  2I70 

2i89 

5o 

9 

8766 

8784 

8802 

8820 

8838 

8857 

5o 

10 

9.8722o8 

2226 

2245  22642283 

23O2  49 

10 

9.878875 

8893 

8911 

8929 

8948 

8966 

49 

ii 

2321 

234o 

2358  2377  2396 

24i548 

ii 

8984 

9002  9020 

9o39 

9o57 

9o75 

48 

12 

2434 

2452 

2471  2490  2509 

2528 

47 

12 

9093 

9111  9129 

9148 

9166 

9184 

47 

-  <: 

2547 

2565  2584  26032622 

264i 

46 

i2 

9202 

9220 

9238 

925-7 

9275 

9293 

46 

i4 

2659 

26-78 

2697  2716  2735 

2753 

45 

i4 

93n 

9329 

9347 

9365 

9384 

9402 

45 

i5 
16 

2772 

2885 

27gi  2810  2829 
2904  2923  2941 

2847 
296o 

2866 
2979 

44 
43 

i5 
16 

9420 
9529 

9438 

9547 

9456 
9565 

9474 
9583 

9^)2 

9601 

95n 

9619 

44 
43 

17 

2998 

3oi63o353o54 

3o73 

3o9i 

42 

i7 

9637 

9656 

9674 

9692J97io 

9728 

42 

18 

3no 

3i293i483i66 

3i85 

3204 

4i 

18 

9746 

9764 

9782 

9800  9819 

9837 

4i 

19 

3223 

324l 

3260  32-79 

3298 

33i6 

4o 

'9 

9855 

9873 

989i 

9909 

9927 

9945 

4o 

20 

9.873335 

33543373339i 

34io 

3429 

39 

20 

9.879963 

998i 

..18 

..36 

..54 

39 

21 

3448 

3466 

3485  35o43522 

354i 

38 

21 

9.880072 

oo9o 

0108 

0126 

0144 

0162 

38 

22 

356o 

3579 

359736i63635 

3653 

37 

22 

0180 

oi98 

0216 

0234 

0253 

027I 

37 

23 

3672 

369i 

37io  3728 

3747 

3766 

36 

23 

0289 

o3o7 

o325 

o343 

o36i 

o379 

36 

24 

3784 

38o3 

3822  384o 

3859 

3878 

35 

24 

o397 

o4i5 

o433 

o45i 

o469 

o487 

35 

25 

3896 

39i5 

3934  3953 

397i 

399o 

34 

25 

o5o5 

o523 

o54i 

o559 

o577 

o595 

34 

26 
27 

4009 

4l2I 

402-7  4o46  4o65 
4i394i584i77 

4o83 
4i95 

4lO2 

42i4 

3S 

32 

26 
27 

o6i3 
0722 

o63i 
o74o 

o649 
o758 

o667 
o776 

0686 
o794 

o7o4 

0812 

33 

32 

28 

4232 

425i  42-704288 

43o7 

4326 

3i 

28 

o83o 

o848 

0866 

o884 

O9O2 

O920 

3i 

29 

4344 

4363  4382  44oo 

44i9 

4438 

3o 

29 

0938 

o956 

o974 

0992 

IOIO 

1028 

3o 

3o 
3i 

9.874456 
4568 

4475449345i2 
4586  46o54624 

453i 
4642 

4549 
466i 

29 

28 

3o 
3i 

9.881046 
n53 

io63 
1171 

1081 
u89 

1099 

I207 

III7 
1225 

n35 
1243 

28 

32 

33 

468o 
4791 

469847i7 
48104828 

4735 
4847 

47544773 
48664884 

27 
26 

32 

33 

1261 
1  369 

I279 

i387 

I297 

i4o5 

i3i5 

1423 

i333 
i44i 

i35i 
i459 

27 
26 

34 
35 

4903 
5oi4 

492i  494o 
5o33  5o5i 

4958 
5o7o 

49774996 
5o885io7 

25 
24 

34 
35 

i477 
1  584 

i495 
1602 

l5l2 

1620 

i53o 
i638 

1  548 
i656 

1  566 
i674 

25 
24 

36 

5i26 

5i445i63 

5i8i 

520052I&23 

36 

1692 

I7IO 

1-728 

i746 

i763 

1-781 

23 

37 

5237 

5255 

5274 

5293 

53n 

533022 

37 

1799 

181-7 

i835 

i853 

18-71 

i889 

22 

38 

5348 

53675385 

54o4 

5422544i 

21 

38 

1907 

1925 

I942 

1960 

1978 

I996 

21 

39 

5459 

5478  5496 

55i5 

55345552 

2O 

39 

1014 

2032 

2o5o 

2068 

2086 

2103 

2O 

4o 

9.87557i 

5589  56o8 

5626 

5645|5663 

I9 

4o 

9.882121" 

2i39 

2l57 

2I75 

2I93 

2211 

J9 

4i 

5682 

57oo 

57i9 

5737 

57565774 

18 

4i 

2229 

2246  2264 

2282 

2300 

23i8 

IS 

42 

5793 

58n  583o 

5848 

58675885 

ll 

42 

2336 

2354  237i 

2389 

2407 

2425 

I7 

43 

59o4 

5922  594i 

5959 

5978  5996 

16 

43 

2443 

2461  2479 

2496 

25i4 

2532 

16 

44 

6oi4 

6o33  6o5i 

6o7o 

6088610-7 

i5 

44 

255o 

2568  2586 

26o3 

2621 

2639 

i5 

45 

6i25 

61446162 

6181 

6199  6218 

i4 

45 

2657 

2675 

2692 

27IO 

2-728 

2746 

i4 

46 

6236 

6255  6273 

629I 

63io6328 

i3 

46 

2764 

2782 

2799 

281-7 

2835 

2853 

i3 

47 

6347 

6365  6384 

6402 

6421  6439 

12 

47 

2871 

2888 

29o6 

2924 

2942 

296o 

12 

48 

6457 

6476  6494 

65i3 

653i  655o 

II 

48 

2977 

2995 

3oi3 

3o3i 

3o49 

3o66 

II 

49 

6568 

6586  66o5 

6623 

66426660 

10 

49 

3o84 

3lO2 

3l20 

3i37 

3i55 

3i73 

10 

5o 

9.876678 

6697  67i5 

6734 

6752  677o 

9 

5o 

9.883191 

3209 

3226 

3244 

3262 

328o 

9 

5i 

6789 

680-76826 

6844 

68626881 

8 

5i 

3297 

33i5 

3333 

335i 

3368 

3386 

8 

52 

6899 

69i8  6936 

6954 

69-73  6991 

7 

52 

34o4 

3422 

3439 

3457 

3475 

3493 

7 

53 

7OIO 

-7028  7o46 

7o65 

7o83  -7101 

6 

53 

35io 

3528 

3546 

3564 

358i  3599 

6 

54 

7120 

7i38  7i57 

7i75 

7I93  72I2 

5 

54 

36i7 

3635 

3652 

367o 

3688  37o5 

5 

55 

723o 

•7248-726-7 

7286 

73o3  7322 

4 

55 

3723 

374i 

3759I3776  3794  38i2 

4 

56 
57 

734o 
745o 

73587377 
7468  7487 

7395 
75o5 

74i37432 

3 

2 

56 

57 

3829 
3936 

3847  3865  3883  39oo  39i8 
3953  39-71  3989^0064024 

3 

2 

58 

756o 

7578  7597 

76i5 

7633  7652 

I 

58 

4o42 

4o6o  4077  4095  4n3  4i3o 

I 

59 

767o  7688  77o77725 

7743  7762 

0 

59 

4i48 

4i66  4i83  4201*4219  4236 

0 

60" 

50"  j 

40"   30" 

20"   10" 

a 

60" 

50"   40"   30"   20"   10"  I 

Co-sine  of  41  Degrees. 

Jl 

is 

Co-sine  of  40  Degrees.     s 

PPartJ1"  2"  3// 

4"  5"  6"  7"  8"  9" 

.<  1"  2"  3"  4"  5"  6"  7"  8"  9" 

"1  a  4  6 

7   9  11  13  15  17 

irl$  24   5   7   9  11  13  14  16 

LOGARITHMIC    TANGENTS. 


73 


1 

Tangent  of  48  Degrees. 

.3 

Tangent  of  49  Degrees. 

2 

0" 

10"   20"  1  30"   40" 

50" 

al 

0" 

10' 

20" 

30" 

40" 

50" 

0 

i 

io.o45563 
58i7 

56o55647569o5732 
585959oi  5944J5986 

5774 
6028 

59 

58 

( 
i 

10.060837 
1092 

o879 
n35 

0922 
1177 

o965 

I22O 

IO07 
1262 

io5o 
i3o5 

59 

58 

2 

6071 

6n36i556i98 

6240 

6282 

57 

9 

1  347 

i39o 

1432 

i475 

i5i7 

i56o 

57 

3 

6325 

6367(64o96452 

6494 

6537 

56 

Q 

1602 

1  645 

1688 

1730 

i773 

i8i5 

56 

4 

6579 

6621  6664  67o6 

6748 

679i 

55 

4 

i858 

I900 

1943 

i985 

2028 

2070 

55 

5 

6833 

6875i69i8J696o]7oo2 

54 

c 

2Il3 

2i55 

2198 

224l 

2283  2326 

54 

6 

7087 

7i3o  7172 

7214  7257 

7299 

53 

6 

2368 

2411 

2453 

2496 

2538258i 

53 

7 

734i 

7384^426 

7468 

75n 

7553 

52 

7 

2623 

2666 

2709 

275l 

2794 

2836 

52 

8 

7595 

7638  7680 

7723 

7765 

78o7 

5i 

8 

2879 

292I 

2964 

3oo6 

3o49 

3o92 

5i 

9 

785oJ7892J7934 

7977 

8019 

8062 

5o 

9 

3  1  34 

3i77 

3219 

3262 

33o4 

3347 

5o 

10 

io.o48io48i468i89 

82  3  1 

8273 

83i6 

49 

10 

10.063389 

3432 

3475 

35i7 

356o 

3bo2 

4y 

1  1 

8358 

84oo 

8443 

8485 

8528 

857o 

48 

ii 

3645 

3687 

373o 

3773 

38i5 

3858 

48 

12 

8612 

8655 

8697 

8739 

8782 

8824 

47 

12 

39oo 

3943 

3985 

4028 

4o7o 

4n3 

47 

i3 

8867 

89o9 

895i 

8994 

9o36 

9©79  46 

i3 

4i56 

4i98 

424i 

4283 

4326 

4368 

46 

i4 

9I2I 

9i63 

9206 

9248 

929o 

9333 

45 

i4 

44n 

4454 

4496 

4539 

458i 

4624 

45 

i5 

9375 

94i8 

946o 

95o2 

9545 

9587 

44 

i5 

4667 

4709 

4?52 

4794 

4837 

4879 

44 

16 

9629 

0.672 

97i4 

97^-7 

9799 

9841 

43 

16 

4922 

4965 

5007 

5o5o 

5o92 

5i35 

43 

17 

9884 

9926 

9969 

..ii 

..53 

..96 

42 

17 

5i78 

522O 

5263 

53o5 

5348 

539o 

42 

18 

io.o5oi38 

0181 

0223 

0265 

o3o8 

o35o 

4i 

18 

5433 

5476 

55i8 

556i 

56o3 

5646 

4i 

19 

o392 

o435 

o477 

0520 

o562 

o6o4 

4o 

19 

5689 

573i 

5774 

58i6 

5859 

59O2 

4o 

20 

io.o5o647 

o689 

0732 

0774 

0816 

o859 

39 

20 

io.o65944 

5987 

6o29 

6o72 

6n5 

6i57 

39 

21 

o9oi 

o944 

o986 

1028 

IO7I 

in3 

38 

21 

6200 

6242 

6285 

6328 

6370 

64i3 

38 

22 

n56 

1198 

1240 

1283 

i325 

i368 

37 

22 

6455 

6498 

654i 

6583 

6626 

6668 

37 

23 

i4io 

1452 

i495 

i537 

i58o 

1622 

36 

23 

6711 

6754 

6796 

6839 

6881 

6924 

36 

24 

i665 

1707 

i749 

1792 

i834 

i877 

35 

24 

6967 

7oo9 

7o52 

7o94 

7i37 

7180 

35 

25 

I9i9 

i96i 

2004 

2046 

2o89 

2l3l 

34 

25 

7222 

7265 

73o8 

735o 

7393 

7435 

34 

26 

2173 

2216 

2258 

2301 

2343 

2386 

33 

26 

7478 

7521 

7563 

76o6 

7649 

•7691 

33 

27 

O./IOQ 

2470 

25i3 

2555 

2598 

2640 

32 

27 

7734 

7776 

7819 

7862 

7904 

7947 

32 

28 

2682 

2725 

2767 

2810 

2852 

2895 

3i 

28 

799° 

8o32 

8o75 

8117 

8160 

8203 

3i 

29 

2937 

2979 

3O22 

3o64 

3io7 

3i49 

3o 

29 

8245 

8288 

833i 

8373 

84i6 

8458 

3o 

3o 

io.c53i92 

3234 

3276 

33i9 

336i 

34o4 

29 

3o 

io.o685oi 

8544 

8586 

8629 

8672 

87i4 

29 

3i 

3446 

3489 

353i 

3573 

36i6 

3658 

28 

3  1 

8757 

8800 

8842 

8885 

8927 

897o 

28 

32 

3701 

3743 

3786 

3828 

387o 

3gi3 

27 

32 

9013 

9o55 

9o98 

9i4i 

9183 

9226 

27 

33 

3955 

3998 

4o4o 

4o83 

4i25 

4i68 

26 

33 

9269 

93n 

9354 

9397 

9439 

948? 

26 

34 

4210 

4252 

4295 

4337 

438o 

4422 

25 

34 

9525 

9567 

96io 

9652 

9696 

9738 

25 

35 

4465 

45o7 

4549 

4592 

4634 

4677 

24 

35 

978o 

9823 

9866 

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995i 

9994 

24 

36 

47i9 

4762 

48o4 

4847 

4889 

493i 

23 

36 

io.o7oo36 

oo79 

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02O7 

O25o 

23 

37 

4974 

5oi6 

5o59 

5ioi 

5i44 

5i86 

22 

37 

0292 

o335 

o378 

O420 

o463 

o5o6 

22 

38 

5229 

527I 

53i4 

5356 

5398 

544i 

21 

38 

o548 

o59i 

o634 

o676 

o7i9 

0762 

21 

39 

5483 

5526 

5568 

56n 

5653 

5696 

20 

39 

o8o4 

0847 

o89o 

0932 

°975 

1018 

20 

4o 

io.o55738 

578i 

5823 

5865 

59o8 

SgSo 

19 

4o 

io.o7io6o 

no3 

n46 

1188 

I23l 

I274 

I9 

4i 

5993 

6o35 

6078 

6120 

6i63 

62o5 

18 

4i 

i3i6 

i359 

I4O2 

i445 

i487 

i53o 

18 

42 

6248 

629o 

6333 

6375 

64i7 

646o 

!7 

42 

i573 

i6i5 

i658 

I7OI 

1743 

i786 

17 

43 

65o2 

6545 

6587 

663o 

66-72 

67i5 

16 

43 

l829 

1871 

i9i4 

i957 

i999 

2O42 

16 

44 

6757 

6800 

6842 

6885 

6927 

697° 

i5 

44 

2o85 

2128 

2170 

22l3 

2256 

2298 

i5 

45 

7OI2 

7o55 

7°97 

7i39 

7182 

i4 

45 

234l 

2384 

2426 

2469 

25l2 

2554 

i4 

46 

7267 

73o9 

7352 

7394 

7437 

7479 

i3 

46 

2597 

2640 

2683 

2725 

2768 

2811 

i3 

47 

'  -  7522 

7564 

76o7 

7692  7734 

12 

47 

2853 

2896 

2939 

298l 

3o24 

3o67 

12 

48 

7777 

7819 

7862 

79°4 

7947|7989 

II 

48 

3no 

3i52 

3i95 

3238 

3280 

3323 

II 

49 

8o32 

8o74 

8n7 

8i59 

8202(8244 

IO 

49 

3366 

34o9 

345  1 

3494 

3537 

3579 

IO 

5o 

io.o58287 

8329 

8372 

84x4 

84568499 

9 

5o 

IO.O73622 

3665 

37o8 

375o 

370.3  3836 

9 

5i 

854i 

8584 

8626 

8669 

87n  8754 

8 

5i 

3878 

392I 

3964 

4oo7 

4o49  4o92 

8 

52 

8796 

8839 

8881 

8924 

8966  9oo9 

7 

52 

4i35 

4178 

4220 

4263 

43o6  4348 

7 

53 
54 

9o5i 
93o6 

9o94 
9349 

9i36 
939i 

9i79 
9434 

922I  9264 

9476  9519 

6 
5 

53 

54 

439i 

4648 

4434 
469o 

4477 
4733 

45i9 
4776 

4562  46o5 
48i9486i 

6 

5 

55 

956i 

96o4 

9646 

9689 

9732 

9774 

4 

55 

49o4 

4947 

4989 

5o32 

5o75j5nd 

4< 

56 

98i7 

9859 

9902 

9944 

9987 

..29 

3 

56 

5i6o 

52o3 

5246 

5289 

533ii5374 

3 

57 

io.o6oo72 

on4 

oi57 

oi99 

0242 

0284 

2 

57 

54i7 

546o 

55o2 

5545 

55885631 

2 

58 

o327 

o369 

O4l2 

o454 

0497 

o539 

I 

58 

5673 

5716 

5759 

58o2 

5844  5887 

I 

59 

o582 

0624 

o667 

o7o9 

0752 

0794 

0 

59 

593o 

5973 

6oi5 

6o58 

6ioi|6i44 

O 

60" 

50" 

40" 

30" 

20" 

10" 

d 

60" 

50" 

40" 

30" 

W  |  10" 

• 

Co-tangent  of  41  Degrees. 

•3 

Co-tangent  of  40  Degrees. 

5 

P  P»rt5  l"  1"  3"  4"  5"  6"  7"  S"  9" 

I  4   8  13  17  21  25  30  34  38 

v  F  .(  1"  2"  3"  4"  5"  6"  7"  8"  9" 
irt}  4   9  13  17  2  X  *'o  30  34  38 

LOGARITHMIC    SINES. 


3 

Sine  of  50  Degrees. 

-a 

Sine  of  51  Degrees. 

4 

*•  ~~  [  10"  I  20" 

I  30"  i  40" 

50" 

51 

0" 

10" 

20" 

30" 

40" 

50" 

O 

9.S84254!4272|4289 

43074325 

4342 

59 

o 

9.89o5o3 

0620 

o537 

o554 

0671 

0688 

59 

I 

436oj4378|4395 

44i3443i 

4448 

58 

I 

0606 

0622 

o639 

0666 

o673 

o69o 

58 

2 

4466 

44S3|45oi 

45i9'4536 

4554 

5? 

2 

0707 

0724 

0741 

0768 

o775 

0792 

57 

"i 

4572 

4589  4007  4626  4642 

466o 

56 

2 

o8o9 

0826 

o843 

0860 

o877 

o894 

56 

L 

4677  4695  47i3 

473o!4748 

476666 

4 

o9n 

O928 

o945 

0962 

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o996 

55 

6 

4783 
4889 

48oi43i8  4836  4854 
49o6  49244942|4959 

487i54 
4977  53 

c 

6 

ioi3 

in5 

io3o 

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1047 
n49 

1064 
1166 

1081 
1  1  83 

1096 
1  200 

54 
53 

7 

4994 

5oi2  5o3o 

5o47!5o65 

6082  62 

7 

1217 

1234 

1261 

1268 

1286 

1302 

52 

8 

5ioo 

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6170 

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8 

i3i9 

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9 

52o5 

6223  6241  6268 

5276[5293 

5o 

9 

1  4s  i 

i438 

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1472 

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10 

9.8853n 

532853465364 

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10 

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1  54o 

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ii 

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ii 

1624 

1  64  1 

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1676 

1692 

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48 

12 

5522 

553955575574 

5592 

56o9 

47 

12 

1-726 

1743 

1760 

1777 

1794 

1810 

47 

t3 

6627 

5644  5662 

5679 

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6714 

46 

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l827 

1  844 

1861 

1878 

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46 

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6732 

5749  5767 

5784 

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6819 

45 

i4 

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1980 

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20l3 

45 

i5 

5837 

5855  68726800 

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44 

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2o3o 

2047 

2064 

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44 

16 

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16 

2l32 

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17 

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6o65  6082 

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42 

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2233 

2260 

2267 

2284 

2300 

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18 

6i52 

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18 

2334 

235i 

2368 

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2620 

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20 

9.  886362 

6379639664i4 

643  1 

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39 

20 

9.892536 

2553 

2670 

2687 

2604 

2621 

39 

21 

6466 

6484  65oi 

65i9 

6536 

6554 

38 

21 

2638 

2664 

2671 

2688 

2706 

2722 

38 

22 

657i 

6588  6606  6623 

664i 

6658 

37 

22 

2739 

2766 

2772 

2789 

2806 

2823 

37 

23 

6676 

6693  6710  6728 

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6763 

36 

23 

2839 

2866 

2873 

2890 

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2924 

36 

24 
25 

6780 
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6860 
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34 

24 
25 

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34 

26 

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7076 

33 

26 

3i42 

3i59 

3i76 

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3209 

3226 

33 

27 
28 

7°93 
7198 

7111  7128  7146 
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7i63 
7267 

7180 
7286 

32 

3i 

27 

28 

3243 
3343 

3259 
336o 

3276 
3377 

3293 
3394 

33io 
34io 

3327 
3427 

32 

3i 

29 

7302 

73197337 

7354 

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7389 

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29 

3444 

346i 

3477 

3494 

35ii 

3528 

3o 

3o 

9.8874o6 

74^3  744i 

7458 

7493 

29 

3o 

9.893544 

356i 

3578 

3595 

36n 

3628 

29 

3i 

75io 

7628  7545 

7562 

758o 

7597 

28 

3i 

3645 

3662 

3678 

3695 

3712 

3728 

28 

32 

7614 

7632  764^7666 

76847701 

27 

32 

3745 

3762 

3779 

3795 

38i2 

3829 

27 

33 

77i8 

77367753:7770 

77877806 

26 

33 

3846 

3862 

3896 

39I2 

3929 

26 

34 

7822 

7839  7857 

7*74 

789Ii79°9 

25 

34 

3946 

3963 

3979 

3996 

4oi3 

4029 

26 

35 

7926 

7943  7961 

7978 

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24 

35 

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24 

36 

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23 

36 

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4i96 

42i3 

423o 

23 

37 

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8i5i  8168 

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22 

37 

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4263 

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433o 

22 

38 

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8289 

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21 

38 

4346 

4363 

438o 

4396 

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21 

3o 

834i 

83588375 

8393 

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39 

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4463 

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4496 

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8462  8479  8496 

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9.  894546 

4563 

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4629 

39 

4i 

8548 

8565  8582 

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18 

4i 

4646 

4663 

4679 

4696 

47i3 

4729 

-8 

42 

865i 

8669  8686|87o3 

87208737 

17 

42 

4746 

4763 

4779 

4796 

4812 

4829 

17 

43 

8755 

8772  8789  8806 

8824  884i 

16 

43 

4846 

4862 

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49I2 

4929 

16 

44 

8858 

8875889289io 

8927  8944 

16 

44 

4945 

4962 

4979 

4995 

5oi2 

6028 

16 

45 

896i 

897889969oi3 

9o3o  9o47 

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45 

5o45 

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6078 

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6111 

6128 

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46 

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9o82  9o99J9ii6 

9i339i5o 

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46 

6146 

6161 

6178 

5i94 

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47 

9i68 

9i85  9202;92I9 

92369253 

12 

47 

6244 

6261 

6277 

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53io 

5327 

12 

48 

9271 

9288  93o5|9322 

93399356 

II 

48 

5343 

536o 

5377 

5393 

54io 

5426 

II 

49 

9374 

939i  94o8 

9425  9442  9459 

10 

49 

5443 

5459 

5476 

5493 

55o9 

6626 

10 

5o 

9.889477 

949495u 

0628  9545  9662 

9 

5o 

9.895542 

5559 

5575 

5592 

56o8 

6626 

9 

5i 

9579 

959796i4 

963i 

9648  9665 

8 

61 

564i 

5658 

5675 

569i 

5708 

6724 

8 

52 

53 

9682 
9785 

969997i6 
98o2  98i9 

973497619768 
983698639871 

6 

62 
53 

574i 
584o 

6767 
5856 

5774 
6873 

6790 

6889 

6807 
59o6 

5823 

5922 

6 

54 

9888 

99o5  9922 

9939199669973 

5 

54 

5939 

5955 

6972 

5988 

6oo5 

6O2I 

5 

55 

999° 

.  .  .7  .  .25 

..42  ..59  ..76 

4 

55 

6o.38 

6o54  6071 

6087 

6io4 

6l20 

4 

56 

57 

9.89oo93 
oi95 

01100127 

0212  O23o 

oi44|0i6i  0178 
0247  0264  0281 

3 

3 

56 

57 

6i37 
6236 

6i53  6170 
6262  6269 

6186 
6286 

62o3 

63o2 

62I9 

63i8 

3 

2 

58 

0298 

o3i5o332 

o349 

o366o383 

I 

58 

6335635i 

6368  6384 

64oo 

64i7 

I 

59 

o4oo 

04170434 

o45i 

o468  o486 

O 

59 

6433 

645o  6466 

6483 

6499  65:6 

0 

60" 

50"  i  40" 

30" 

20"   10" 

ES 

60" 

50"  |  40" 

30" 

20"  i  10" 

G 

Co-sine  of  39 

Degrees. 

JB 

s 

Co-sine  of  38  Degrees     s 

(  111   O"   «J"   A" 

P-Part{2   3   5   7 

5"  6"  7"  8"  9" 
9  10  12  14  16 

C  1"  2"  3"  4"  5"  6"  7"  8"  9" 
1  I  2   3   5   7   8  10  12  13  15 

LOGARITHMIC    TANGENTS. 


75 


d 

•fH 

Tangent  of  50  Degrees. 

d 

Tangent  of  51  Degrees. 

3 

0" 

10" 

20" 

30" 

40" 

50" 

'^ 

0" 

10" 

20"  1  30"  |  40" 

50" 

0 

10.076186 

6229 

6272 

63i5 

6358 

64oo 

59J 

o 

10.091631 

1674 

1717 

I76o 

i8o3 

1846 

59 

I 

6443 

6486 

6529 

657i 

66i4 

6657 

58 

i 

1889 

I932 

I975 

2018 

2061 

2IO4 

58 

2 

6700 

6742 

6785 

7828 

687i 

6913 

57 

2 

2147 

2191 

2234 

2277 

2320 

2363 

57 

3 

6956 

6999 

7042 

7o85 

-712-7 

71-70 

56 

3 

2406 

2449 

2492 

2535 

2578 

2621 

56 

4 

7213 

7256 

7298 

734i 

7384 

742-7 

55 

4 

2664 

2707 

275o 

2793 

2837 

2880 

55 

5 

7470 

7512 

7555 

7598 

764i 

7684 

54 

5 

2923 

2966 

3009 

3o52 

3o95 

3i38 

54 

6 

77*5 

7769 

7812 

7855 

7897 

794o 

53 

6 

3i8i 

3224 

3267 

33io 

3354 

3397 

53 

7 

7983 

8026 

8069 

8m 

8i54 

8197 

52 

7 

344o 

3483 

3526 

3569 

36i2 

3655 

52 

8 

8240 

8283 

8325 

8368 

84n 

8454 

5i 

8 

3698 

374i 

3784 

3828 

387i 

39i4 

5i 

9 

8497 

8539 

8582 

8625 

8668 

8711 

5o 

9 

3957 

4ooo 

4o43 

4o86 

4i29 

4172 

5o 

10 

10.078753 

8796 

8839 

8882 

8925 

8967 

49 

10 

i  0.0942  i  5 

4259 

43o2 

4345 

4388 

443  1 

^9 

ii 

9010 

9o53 

9o96 

9i39 

9181 

9224 

48 

ii 

4474 

45i7 

456o 

46o3 

4647 

4690 

i8 

12 

9267 

93io 

9353 

9396 

9438 

948  1 

47 

12 

4733 

4776 

4819 

4862 

49o5 

4948 

47 

i3 

9524 

9567 

9610 

9652 

9695 

9738 

46 

i3 

4992 

5o35 

5o78 

5l2I 

5i64 

5207 

46 

i4 

9781 

9824 

9867 

99°9 

9952 

9995 

45 

i4 

525o 

5293 

5337 

538o 

5423 

5466 

45 

i5 

io.o8oo38 

0081 

0124 

0166 

0209 

0252 

44 

i5 

55o9 

5552 

5595 

5638 

5682 

5725 

44 

16 

0295 

o338 

o38i 

o423 

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oSog 

16 

5768 

58n 

5854 

5897 

5940 

5984 

43 

17 

o552 

o595 

o638 

0680 

0723 

0766 

42 

17 

6027 

6070 

6n3 

6i56 

6199 

6242 

[2 

18 

0809 

o852 

o895 

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0980 

1023 

4i 

18 

6286 

6329 

6372 

64i5 

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ii 

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1066 

1  109 

1162 

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19 

6544 

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6674 

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20 

io.o8i323 

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39 

20 

io.o968o3 

6847 

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6933 

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39 

21 

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1623 

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21 

7062 

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22 

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22 

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23 

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23 

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24 

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35 

24 

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35 

25 

2609 

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2823 

34 

25 

8099 

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34 

26 

2866 

2909 

2952 

2996 

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3o8i 

33 

26 

8358 

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8444 

8487 

853i 

8574 

33 

27 

3i23 

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3209 

3252 

3295 

3338 

32 

27 

8617 

8660 

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8833 

32 

28 

338i 

3424 

3467 

3509 

3552 

3595 

3i 

28 

8876 

8919 

8963 

9006 

9049 

9092 

3i 

29 

3638 

368i 

3724 

3767 

38io 

3853 

3o 

29 

9i36 

9179 

9222 

9265 

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3o 

3o 

10.083896 

3938 

398i 

4024 

4o67 

4no 

29 

So 

10.099395 

9438 

948  1 

9524 

9568 

9611 

29 

3i 

4i53 

4196 

4239 

4282 

4325 

4367 

28 

3i 

9654 

9697 

974i 

9784 

9827 

9870 

28 

32 

44io 

4453 

4496 

4539 

4582 

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27 

32 

99i3 

9957 

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..86 

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27 

33 

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4754 

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4839 

4882 

26 

33 

10.  100173 

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0259 

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26 

34 

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25 

34 

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35 

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24 

36 

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23 

36 

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1124 

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23 

37 

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574i 

5784 

5827 

587o 

59i3 

22 

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1254 

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1  384 

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22 

38 

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6o84 

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21 

38 

1470 

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1600 

1  643 

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21 

39 

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20 

39 

1730 

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1860 

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10.086471 

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6600 

6643 

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10.  ioi99o 

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2119 

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2206 

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6729 

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6900 

6943 

18 

4i 

2249 

2293 

2336 

2422 

2466 

18 

42 

6986 

7029 

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7ii5 

7i58 

7201 

17 

42 

25o9 

2552 

2596 

2639 

2682 

2725 

17 

43 

7244 

7287 

733o 

7373 

74i6 

7459 

16 

43 

2769 

2812 

2855 

2899 

2942 

2985 

16 

44 

7502 

7588 

763i 

7674 

7717 

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44 

3o29 

3o72 

3n5 

3i58 

3202 

3245 

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45 

7760 

78o3 

7846 

7889 

7932 

7975 

i4 

45 

3288 

3332 

3375 

34i8 

3462 

35o5 

i4 

46 

8018 

8o6l 

8  10^ 

8i47 

8i9o 

8232 

i3 

46 

3548 

3592 

3635 

3678 

3722 

3765 

i3 

47 

8275 

83i8 

836i 

84o4 

8447 

849o 

12 

47 

38o8 

385i 

3895 

3938 

3981 

4o25 

12 

48 

8533 

8576 

8619 

8662 

87o5 

8748 

II 

48 

4o68 

4n  i 

4i55 

4i98 

4241 

4285 

II 

49 

8791 

8834 

8877 

8920 

8963 

9006 

10 

49 

4328 

4371 

44i5 

4458 

45oi 

4545 

10 

5o 

10.089049 

9092 

9i35 

9i78 

922I 

9264 

9 

5o 

i  o.i  o4588 

463  1 

4675 

4718 

4761 

48o5 

9' 

5i 

9307 

935o 

9393 

9436 

94?9 

9522 

8 

5i 

4848 

489i 

4935 

4978 

5O2I 

5o65 

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52 

9565 

9608 

9694 

9737 

978o 

7 

52 

6108 

5i52 

5i95 

5238 

5282 

5325 

7 

53 

9823 

9866 

9909 

9952 

9995 

..39 

6 

53 

5368 

54i2 

5455 

5498 

5542 

5585 

6 

54 

10.090082 

0125 

0168 

0211 

025^ 

0297 

5 

54 

56a8 

5672 

57i5 

5759 

58o2 

5845 

5 

55 

o34o 

o383 

0426 

0469 

o5i2 

o555 

4 

55 

5889 

5932 

5975 

6019 

6062 

6106 

4 

56 

o598 

o64i 

o684 

O727 

o77o 

o8i3 

3 

56 

6149 

6i9a 

6236 

62-79 

6322 

6366 

3 

57 

o856 

0899 

0942 

o985 

1028 

1071 

a 

57 

6409 

6453 

6496 

6539 

6580 

6626 

2 

58 

ni4 

ii57 

1  200 

1243 

1286 

i329 

i 

58 

6669 

67i3 

6756 

6800 

6843 

6886 

I 

59 

I372 

i4i6 

1459 

1502 

1  545 

1688 

o 

59 

6980 

6973 

7oi7 

-7060 

7io3 

7i47 

O 

60" 

50" 

40" 

30" 

20" 

10" 

. 

60" 

50" 

40" 

30" 

20" 

10" 

d 

Co-tangent  of  39  Degrees. 

i 

Co-tangent  of  38  Degrees. 

a 

p  p  .  <  1"  2"  3"  4"  5"  6"  7"  8"  9" 
irt{  4   9  13  17  21  26  30  34  39 

P.  Part  |  4   9  13  17  22  26  30  35  39 

LOGARITHMIC    SINES. 


.g 

Sine  of  52  Degrees. 

.H 

Sine  of  53  Degrees. 

a 

0" 

10" 

20" 

30" 

40"  |  50" 

SI 

0" 

10"   20"   30" 

40" 

50" 

o 

9.896532 

6549 

6565658i 

6598  6614)59 

o 

9.9o2349  2364 

238o 

2396 

24l2 

2428 

59 

I 

2 

663i  6647 
67296746 

6664  6680 
6762  6779 

669-7  67i3 
6-7956812 

58 

i 

2 

2444 
2539 

246o 

2555 

2475 
2571 

2491 

2586 

25o7 
2602 

2523 

2618 

58 
57 

3 

68286844 

6861 

6877 

6894  6910 

56 

3 

2634 

265o 

2666 

2681 

2697 

27l3 

56 

4 

6926  6943 

6959 

6976 

6992  -7009 

55 

4 

2729 

2745 

2761 

2776 

2792 

2808 

55 

5 

7025 

704  1 

7o58 

7o74 

7o9o7io7 

54 

5 

2824 

2840 

2856 

2871 

2887 

29o3 

54 

6 

7I23 

7i4o 

7i567i72 

7i89!72o5 

53 

6 

2919 

2935 

2950 

2966 

2982 

2998 

53 

7 

7222 

7238 

7254 

727I 

7287  73o3 

52 

7 

3oi4 

3o29 

3o45 

3o6i 

3o77 

3o93 

52 

8 

7320 

7336 

7353 

7369 

7385  74o2 

5i 

8 

3io8 

3i24 

3i4o 

3i56 

3i7i 

3i87 

5i 

9 

74i8 

7434 

745  1 

7467 

7483  75oo 

5o 

9 

32o3 

3219 

3235 

325o 

3266 

3282 

5o 

10 

9.8975i6 

7533 

7549 

7565 

7582  -7598 

49 

10 

9.903298 

33i3 

3329 

3345 

336i 

3377 

49 

ii 

76i4 

763i 

7647 

7663 

-7680  -7696 

48 

ii 

3392 

34o8 

3424 

344o 

3455 

48 

12 

7712 

7729 

7745 

7761 

77787794 

47 

12 

3487 

35o3 

35i8 

3534 

355o 

3566 

47 

i3 

7810 

7827 

7843 

7859 

78767892 

46 

i3 

358i 

3597 

36i3 

3629 

3644 

366o 

46 

i4 

79o8 

7924 

794i 

7957 

7973  799° 

45 

i4 

3676 

369i 

37o7 

3723 

3739 

3754 

45 

i5 

8006 

8022 

8o39 

8o55 

8o7i  8088 

44 

i5 

377o 

3786 

38o2 

38i7 

3833 

3849 

44 

16 

8io4 

8120 

8i368i53 

8i69'8i85 

43 

16 

3864 

388o 

3896 

3912 

3927 

3943 

43 

17 

8202 

8218 

8234 

825o 

8267|8283 

42 

i7 

3959 

3974 

399o 

4oo6 

4021 

4o37 

42 

18 

8299 

83i5 

8332 

8348 

8364838i 

4i 

18 

4o53 

4069 

4o84 

4ioo 

4u6 

4i3i 

4i 

i9 

8397 

84i3 

8429 

8446 

84628478 

4o 

i9 

4i47 

4i63 

4178 

4194 

4210 

4225 

4o 

2o|9.898494 

85n 

85278543 

8559  8576 

39 

20 

9.904241 

4257 

4272 

4288 

43o4 

43i9 

39 

21 

8592 

8608 

86248641 

8657:8673 

38 

21 

4335 

435i 

4366 

4382 

4398 

44i3 

38 

22 

8689 

87o6 

87228738 

8754877o 

37 

22 

4429 

4445 

446o 

44?6 

4492 

45o7 

37 

23 

8787 

88o3 

88i98835 

8852  8868 

36 

23 

4523 

4539 

4554 

457o 

4586 

46oi 

36 

24 

8884 

89oo 

89i68933 

8949  8965 

35 

24 

46i7 

4632 

4648 

4664 

4679 

4695 

35 

25 

898i 

8997 

9oi49o3o 

9046  9062 

34 

25 

4711 

4726 

4742 

4757 

4773 

4789 

34 

26 

9o78 

9o95 

9111 

9I27 

91439159 

33 

26 

48o4 

4820 

4836 

485i 

4867 

4882 

33 

27 

9i76 

9I92 

92O8  9224 

92409256 

32 

27 

4898 

49144929 

4945 

496o 

4976 

32 

28 

9273 

9289 

932I 

93379354 

3i 

28 

4992 

5oo/  5oa3 

5o38 

5o54 

5o7o 

3i 

29 

937o 

9386 

94o2  94i8 

9434945o 

3o 

29 

5o85 

5ioi 

5n6 

5i32 

5i48 

5i63 

3o 

3o 

9.899467 

9483 

9499  95i5 

953i 

9547 

29 

3o 

9.905179 

5i94 

52IO 

5225 

524i 

5257 

29 

3i 

9564 

958o 

9596  96i2 

9628 

9644 

28 

3i 

5272 

5288 

53o3 

53i9 

5334 

535o 

28 

32 

966o 

9677 

9693 

9-709 

9725  974i 

27 

32 

5366 

538i 

5397 

54i2 

5428 

5443 

27 

33 

9757 

9773 

9789  98o6 

9822  9838 

26 

33 

5459 

5474 

5490 

55o6 

552i 

5537 

26 

34 

9854 

987o 

9886  9902 

99i8 

9935 

25 

34 

5552 

5568 

5583 

5599 

56i4 

563o 

25 

35 

995i 

9967 

99839999 

24 

35 

5645 

566i 

5676 

5692 

57o8 

5723 

24 

36 

9.9ooo47 

oo63 

oo79  oo96 

OII2 

0128 

23 

36 

5739 

5754 

577o 

5785 

58oi 

58i6 

23 

37 

oi44 

0160 

01-76  0192 

0208 

0224 

22 

37 

5832 

5847 

5863 

5878 

5894 

59o9 

22 

38 

0240 

0256 

O272 

0289  o3o5 

0321 

21 

38 

5925 

594o 

5956 

597i 

5987 

6002 

21 

39 

o337 

o353 

o369o385 

o4oi 

0417 

2O 

39 

6018 

6o33  6049 

6o64 

6080 

6o95  20 

4o 

9.900433 

o449 

o465o48i 

o497 

o5i3 

I9 

4o 

9.9o6m 

61266142 

6i57 

6i73 

6188 

I9 

4i 

0529 

o545 

o562o578 

o594 

0610 

18 

4i 

6204 

6219 

6235 

625o 

6265 

6281 

18 

42 

0626 

0642 

o658o674o69o 

o7o6 

17 

42 

6296 

63i2 

6327 

6343 

6358 

6374 

17 

43 

O722 

o738 

o754  o77o  o786 

0802 

16 

43 

6389 

64o5 

6420 

6436 

645  1 

6466 

16 

44 

O8l8 

o834 

o85o  0866  0882 

o898 

i5 

44 

6482 

6497 

65i3 

6528 

6544 

6559 

i5 

45 

0914 

o93o 

o946  o962 

o978 

o994 

i4 

45 

6575 

659o  66o5 

6621 

6636 

6652 

i4 

46 

1010 

1026 

1042  io58 

io74 

io9o 

i3 

46 

6667 

6683  6698 

67i3 

6729 

6744 

i3 

47 

1  1  06 

I  122 

n38 

1  1  54 

II70 

1186 

12 

47 

6760 

6775 

6791 

6806 

6821 

6837 

12 

48 

1202 

1218 

1234  I25o 

1266 

1282 

II 

48 

6852 

6868 

6883 

6898 

69i4 

6929 

II 

49 

1298 

i3i4 

i33o 

1  346 

i362 

i378 

IO 

49 

6945 

6960 

6975 

6991 

7006 

7022 

IO 

5o 

9.901394 

i4io 

1426 

1442 

i458 

i474 

9 

5o 

9.9o7o37 

7o52 

-7068 

7o83 

7°99 

7n4 

9 

5i 

1490 

i5o5 

i5ai 

i537 

r553 

i569 

8 

5i 

7I29 

7i45 

7i6o 

7i75 

7i9i 

7206 

8 

52 

i585 

1601 

1617 

i633 

i649 

i665 

7 

52 

7222 

?237 

7252 

7268 

7283 

7298 

7 

53 

1681 

i697 

I7i3 

I729 

i745 

i76o 

6 

53 

73i4 

7329 

7344 

736o 

7375 

739i 

6 

54 

i776 

I792 

1808 

1824 

i84o 

i856 

5 

54 

7406 

742i 

7437 

7452 

7467 

7483 

5 

55)    i872 

1888 

i9o4 

1920 

i936 

i95i 

4 

55 

7498 

75i3 

7529 

75447559 

7575 

4 

56 

196-7 

i983 

i999 

2Ol5 

2031 

2047 

3 

56 

759O 

76o5 

-7621 

7636  765i 

7667 

3 

57 

2o63 

2079 

2O95 

2IIO 

2126 

2142 

2 

57 

7682 

7697 

77i3 

7728  7743 

7759 

2 

58 

2i58 

2I74 

2I9O 

22O6|2222 

2238 

I 

58 

7774 

7789 

78o5 

782o  7835 

785i 

I 

59 

2253 

2269 

2285 

2301  23l7 

2333 

O 

59 

7866 

7881 

7896 

79I2  7927 

7942 

0 

60" 

50" 

40' 

30"  |  20" 

10" 

O 

60"     50" 

40" 

30"  i  20" 

10" 

a 

Co-sine  of  97 

Degrees. 

Co-sine  of  36  Degrees. 

1 

P  PartJ  l"  2"  3//  * 

5"  6"  7"  8"  9" 

p  p  .  <  1"  2"  3"  4"  5"  6"  7"  8"  9" 

l.PartJ  2356 

8  10  11  13  15 

irt\  2   3   5   6   8   9   11  12  14 

LOGARITHMIC    TANGENTS. 


77 


.5 

.  Tangent  of  52  Degrees. 

.5 

Tangent  of  53  DC  grees. 

8 

0" 

10" 

20"  |  30" 

40"   50" 

2 

0" 

10" 

20" 

30' 

40" 

50" 

0 

10.  107190 

7234 

7277(7320 

7364 

7407 

5o 

0 

10.122886 

2929 

2973 

3o  £7 

3o6i 

3io5 

59 

i 

745  1 

7494 

7537758i 

•7624 

7668 

58 

I 

3i48 

3192 

3236 

3280 

3324 

3368 

58 

2 

7711 

7754 

7798  784i 

7885 

7928 

57 

2 

34n 

3455 

3499 

3543 

3587 

363o 

57 

3 

•79-72 

8oi5  8o58 

8l02 

8i458i89 

56 

3 

3674 

37i8 

3-762 

38o6 

385o 

3893 

56 

4 

8275 

83i9 

8362 

84o6  8449 

55 

4 

3937 

398i 

4o25 

4069 

4n3 

4i57 

55 

5 

84g3 

8536 

8579 

8623 

8666 

8710 

54 

5 

4200 

4244 

4288 

4332 

4376 

4420 

54 

6 

8753 

8797 

884o 

8884 

892-7 

8970 

53 

6 

4463 

4507 

455i 

4595 

4639 

4683 

53 

7 

9014 

9101 

9144 

9188 

923l 

52 

7 

4727 

i77o 

48i4 

4858 

1902 

4g46 

52 

8 

9275 

93i8 

936i 

94o5 

9448 

9492 

5i 

8 

499o 

5o34 

5o77 

5l2I 

5i65 

5209 

5i 

9 

9535 

9579 

9622 

9666 

9709 

9753 

5o 

9 

5253 

5297 

534i 

5385 

5428 

5472 

5o 

10 

o.  io9796 

984o 

9883 

9926 

9970 

,.i3 

49 

10 

io.i255i6 

556o 

56o4 

5648 

5692 

5736 

49 

ii 

o.  noo57 

OIOO 

oi44 

0187 

023l 

0274 

48 

ii 

5780 

5823 

5867 

59n 

5955 

5999 

48 

12 

o3i8 

o36i 

o4o5 

o.448 

0492 

o535 

47 

12 

6o43 

6087 

6i3i 

6I?5 

62I9 

6262 

47 

i3 

o579 

0622 

0666 

0709 

0752 

0796 

46 

i3 

63o6 

635o 

6394 

6438 

6482 

6526 

46 

i4 

o839 

o&83 

0926 

0970 

ioi3 

io57 

45 

i4 

6570 

66i4 

6658 

6701 

6745 

6789 

45 

i5 

I  I  00 

1  44 

1187 

I23l 

1274 

i3i8 

44 

i5 

6833 

6877 

6921 

6965 

7009 

7o53 

44 

16 

i36i 

4o5 

1  448 

1492 

i535 

l579 

43 

16 

7097 

7141 

7i85 

7229 

7273 

7816 

43 

ll 

1622 

666 

1709 

i753 

1797 

i84o 

42 

17 

736o 

r4o4 

7448 

7492 

7536 

758o 

42 

18 

1884 

927 

1971 

20l4 

2o58 

2101 

4i 

18 

7624 

7668 

77I2 

7756 

7800 

7844 

4i 

19 

2i45 

2188 

2232 

2275 

23i9 

2362 

4o 

19 

7888 

7932 

7976 

8020 

8o63 

8107 

4o 

20 

o.  112406 

2449 

2493 

2536 

258o 

2623 

39 

20 

10.  I28i5i 

8i95 

8239 

8283 

8327 

8871 

39 

21 

266-7 

2711 

2754 

2798 

2841 

2885 

38 

21 

84i5 

8459 

85o3 

854? 

SSgi 

8635 

38 

22 

2928 

2972 

3oi5 

3o59 

3  I  02 

3i46 

37 

22 

8679 

8723 

8767 

8811 

8855 

8899 

37 

23 

3i89 

3233 

3277 

3320 

3364 

34o7 

36 

23 

8943 

8987 

9075 

9119 

9i63 

36 

24 

345  1 

3494 

3538 

358i 

3625 

3669 

35 

24 

9207 

9251 

9295 

9339 

9383 

9427 

35 

25 

37I2 

3756 

3799 

3843 

3886 

393o 

34 

25 

9471 

95i5 

9559 

96o3 

9647 

9691 

34 

26 

3974 

4017 

4o6i 

4io4 

4i48 

4191 

33 

26 

9735 

9779 

9823 

9867 

9911 

9955 

33 

27 

4235 

4279 

4322 

4366 

44o9 

4453 

32 

27 

9999 

..43 

..87 

.i3i 

.i75 

.2I9 

32 

28 

4496 

454o 

4584 

4627 

4671 

4714 

3i 

28 

io.i3o263 

0307 

o35i 

o395 

0439 

o483 

3i 

29 

4758 

4802 

4845 

4889 

4932 

4976 

3o 

29 

0527 

o57i 

o6i5 

o659 

o7o3 

0747 

3o 

3o 

IO.  Il5o20 

5o63 

5107 

5i5o 

5  1  94 

5238 

29 

3o 

10.  130791 

o835 

o879 

0923 

0967 

ion 

29 

3i 

5281 

5325 

5368 

54i2 

5456 

5499 

28 

3i 

io55 

1099 

n43 

1187 

1232 

1276 

28 

32 

5543 

5586 

563o 

5674 

5717 

576i 

27 

32 

1320 

1  364 

i4o8 

i452 

i496 

i54o 

27 

33 

58o4 

5848 

5892 

5g35 

5979 

6o23 

26 

33 

1  584 

1628 

1672 

1716 

1760 

1804 

26 

34 

6066 

6110 

6i53 

619-7 

6241 

6284 

25 

34 

1  848 

1892 

i936 

1981 

2O25 

2o69 

25 

35 

6328 

6372 

64i5 

6459 

65o2 

6546 

24 

35 

91*3 

2i57 

22OI 

2245 

2289 

2333 

24 

36 

o5oo 

6633 

6677 

672I 

6764 

6808 

23 

36 

2377 

2421 

2465 

2509 

2554 

2598 

23 

37 

6852 

6895 

6939 

6982 

7026 

7070 

22 

37 

2642 

2686 

2780 

2774 

2818 

2862 

22 

38 

7n3 

7l57 

7201 

7244 

7288 

7332 

21 

38 

2906 

2g5o 

2994 

3o39 

3o83 

3!27 

21 

39 

7375 

7419 

7463 

75o6 

755o 

7594 

20 

39 

3i7i 

32I5 

3259 

33o3 

3347 

3391 

2O 

4o 

io.n7637 

7681 

7725 

7768 

7812 

7856 

I9 

4o 

10.  133436 

348o 

3524 

3568 

36i2 

3656 

19 

4i 

7899 

7943 

7987 

8o3o 

8o74 

8118 

18 

4i 

8700 

3?44 

3789 

3833 

3877 

8921 

18 

42 

8161 

82o5 

8249 

8202 

8336838o 

:7 

42 

3965 

4009 

4o53 

4097 

4i42 

4i86 

i7 

43 

8423 

8467 

85n 

8555 

8598 

8642 

16 

43 

4230 

4274 

43i8 

4362 

44o6 

445  1 

16 

44 

8686 

8729 

8773 

88i7 

8860 

8904 

i5 

44 

4495 

4539 

4583 

4627 

467i 

47i5 

i5 

45 

8948 

8992 

9o35 

90-79 

9123 

9166 

i4 

45 

476o 

48o4 

4848 

4892 

4g36 

498o 

i4 

46 

92IO 

9254 

9297 

934i 

9385 

9429 

i3 

46 

5o25 

5o69 

5ii3 

5i57 

52OI 

5245 

i3 

47 

48 

9472 
9735 

95.6 

9778 

956o 

9822 

9602 
9866 

9647 
99°9 

9691 
9953 

12 
I  I 

47 
48 

5290 
5555 

5334 
5599 

5378 
5643 

5422 
5687 

5466 
573i 

55io 
5775 

12 
II 

49 

9997 

..84 

.128 

.172 

?2i6 

10 

49 

5820 

5864 

59o8 

5952 

5996 

6o4i 

10 

5o 

IO.  120259 

o3o3 

o347 

oSgi 

o434 

0478 

g 

5o 

io.i36o85 

6i29 

6178 

6217 

6262 

63o6 

9 

5i 

O522 

o565 

o6o9 

o653 

o697 

0740 

8 

5i 

635o 

63g4 

6438 

6483 

6527 

657i 

8 

52 

o784 

0828 

0872 

ogiS 

o959 

100: 

7 

52 

66i5 

6659 

6704 

6748 

6792 

6836 

7 

53 

io47 

1091 

n34 

11-78 

1222 

1266 

6 

53 

6881 

6925 

6969 

7oi3 

7°57 

7IO2 

6 

54 

1309 

i353 

i397 

i44i 

1  484 

i528 

5 

54 

7146 

7190 

723^ 

7279 

73237367 

1  f 

55 

l572 

1616 

i659 

i7o3 

1747 

1791 

4 

55 

74n 

7455 

75oo 

7544 

7588 

7632 

4 

56 

i835 

1878 

I922 

1966 

2OIO 

2o5!: 

3 

56 

7677 

7721 

7765 

7809 

7854 

7898 

3 

57 

2O97 

2r4i 

2i85 

2229 

2272 

23i6 

2 

57 

7942 

7986 

8o3i 

8075 

8119 

8i63 

2 

58 

236o 

2404 

2448 

2491 

2535 

2^79 

I 

58 

8208 

8252 

8296 

834i 

8385 

8429 

I 

59 

2623 

2667 

2710 

275/! 

2798 

2842 

0 

59 

84?3 

85i8 

8562 

8606 

865o 

8695 

O 

60" 

50" 

40" 

30" 

20" 

10" 

d 

60" 

50" 

40" 

30" 

20" 

10" 

-• 

Co-tangent  of  37  Degrees. 

1 

Co-tangent  of  36  Degrees. 

1 

A  1"  2"  3"  4"  5"  6"  7"  8"  9" 
in\  4   9  13  17  22  26  31  35  39 

<  1"  2"  3"  4"  5"  6"  7"  8"  9" 
l-.-farWj  4   9  13  is  22  26  31  35  40 

78 


LOGARITHMIC    SINES. 


I 

Sine  of  54  Degrees. 

a 

Sine  of  55  Degrees. 

i 

s 

0" 

10" 

20"   30"   40" 

50" 

0" 

10" 

20"   30"  j  40" 

50" 

0 

9.907958 

7973 

798880048019 

8o34 

59 

o 

9.9i3365 

3379 

3394 

34o9  3423 

3438 

59 

I 

8o49 

8o65  80808095  8111 

8126 

58 

i 

3453 

3468 

34S2 

3497 

35i2 

3527 

5S 

2 

8i4i 

8156:817281878202 

821-7 

57 

2 

354i 

3556 

357i 

3585 

36oo 

36i5 

57 

q 

8233 

8248  8263  82-79  8294 

8309 

56 

3 

363o 

3644 

3659 

3674 

3688 

37o3 

56 

4 

8324 

834o!8355837o8385 

84oi 

55 

4 

37i8 

3733 

3747 

3762 

3777 

379i 

55 

c 

84i6 

843  1 

8446  8462:8477)8492 

54 

5 

38o6 

382i 

3836 

385o 

3865 

388o 

54 

6 

8507 

8523 

85388553^85688584 

53 

6 

3894 

39o9 

3924 

3938 

3953 

3968 

53 

7 

8599 

86i4 

86298644:86608675 

52 

7 

3982 

3997 

4012 

4026 

4o4i 

4o56 

52 

8 

869o 

87o5 

8721  87368751)8766 

5i 

8 

4070 

4o85 

4ioo 

4n4 

4129 

4x44 

5i 

9 

8781 

8797 

88128827884218857 

5o 

9 

4i58 

4i73 

4i88 

4202 

4217 

4232 

5o 

JO 

9.908873 

8888 

89038918,8933 

8949 

49 

10 

9.914246 

4261 

42-76 

4290 

43o5 

4320 

49 

ii 

8964 

8979 

89949009*9025 

9040 

48 

ii 

4334 

4349 

4364 

4378 

4393 

4407 

48 

12 

9o55 

90-70  9o85  9101  9116 

9i3i 

47 

12 

4422 

4437 

445  1 

4466 

448  1 

4495 

47 

i3 

9146 

9161 

9176  9192:9207 

9222 

46 

i3 

45io 

4524 

4539 

4554 

4568 

4583 

46 

i4 

9237 

9252 

9267  9283^9298 

93i3 

45 

i4 

4598 

46l2 

4627 

464i 

4656 

467i 

45 

i5 

9328 

93439358:93-7419389 

94o4 

44 

i5 

4685 

47oo 

47i4 

4729 

4744 

4758 

44 

16 

9419 

9434 

9449  9464  9480 

9495 

43 

16 

4773 

4787 

4802 

48i7 

483i 

4846 

43 

17 

952595409555 

957° 

9586 

42 

17 

486o 

4875 

489o 

4904 

4919 

4933 

42 

18 

9601 

96169631  96469661 

9676 

4i 

18 

4948 

4962 

4977 

4992 

5oo6 

5021 

4i 

20 

9691 
9.909782 

97o7972297379752 
9797  9812^827  9843 

9767 
9858 

4o 
39 

'9 

20 

5o35 
9.915123 

5o5o 
5i37 

5o64 
5i52 

5o79 
5i66 

5o94 
5i8i 

5io8 
5i96 

4o 
39 

21 

9873 

9888  99o3 

9918  9933 

9948 

38 

21 

52IO 

5225 

5239 

5254 

5268 

5283 

38 

22 

9963 

997s  9994 

...9 

..24 

..39 

37 

22 

5297 

53i2 

5326 

534i 

5356 

537o 

37 

23 

9.910054 

0069  0084 

0099  01  14 

0129 

36 

23 

5385 

5399 

54i4 

5428 

5443 

5457 

36 

24 

oi44 

oi59  oi75 

0190  O2o5 

O22O 

35 

24 

5472 

5486 

55oi 

55i5 

553o 

5544 

35 

25 

0235 

O25o  O265 

0280 

0295 

o3io 

34 

25 

5559 

5573 

5588 

56o2 

56i7 

563i 

34 

26 

o325 

o34oo355 

0370 

o385 

o4oo 

33 

26 

5646 

566o 

5675 

5689 

57o4 

57i8 

33 

27 

o4i5 

o43oo446 

o46i 

0476 

o49i 

32 

27 

5733 

5747 

5762 

5776 

5791 

58o5 

32 

28 

o5o6 

O52I 

o536 

o55i 

o566o58i 

3i 

28 

5820 

5834 

5849 

5863 

5878 

5892 

3i 

29 

0596 

0611 

0626 

o64i 

06560671 

3o 

29 

59o7 

592I 

5936 

595o 

5965 

5979 

3o 

3o 

9.910686 

O7OI 

0716 

o73i 

o746 

o76i 

29 

3o 

9.915994 

6008 

6023 

6037 

6o52 

6066 

29 

3i 

0776 

o79i 

0806 

0821 

o836 

o85i 

28 

3i 

6081 

6o95 

6109 

6124 

K6i38 

6i53 

28 

32 

0866 

0881 

0896 

0911 

0926 

0941 

27 

32 

6167 

6182 

6196 

6211 

6225 

6240 

27 

33 

0956 

09-71 

0986 

IOOI 

1016 

io3i 

26 

33 

6254 

6268 

6283 

6297 

63i2 

6326 

26 

34 

io46 

1061 

1076 

1091 

1106 

I  121 

25 

34 

634i 

6355 

6369 

6384 

6398 

64i3 

25 

35 

n36 

u5i 

1166 

1181 

1196 

I2II 

24 

35 

6427 

6442 

6456 

6470 

6485 

6499 

24 

36 

1226 

1241 

1256 

1271 

1286 

i3oo23 

36 

65i4 

6528 

6543 

6557 

6571 

6586 

23 

37 

i3i5 

i33o 

i345 

i36o 

1375  139022 

37 

6600 

66i5 

6629 

6643 

fi658 

6672 

22 

38 

i4o5 

1420  i435 

i45o 

i465  i48o 

21 

38 

6687 

6701 

67i5 

6730 

6744 

0759 

21 

39 

1495 

i5io 

i525 

i54o 

i555i569 

2O 

39 

6773 

6787 

6802 

6816 

683o 

6845 

20 

4o 

9.911584 

l599 

i6i4 

1629 

i644  i659  19 

4o 

9.916859 

6874 

6888 

6902 

6917 

693i 

r9 

4i 

1674 

1689 

1704 

1719 

1734  1748  18 

4i 

6946 

696o 

6974 

6989 

7003 

7017 

1  8 

42 

1763 

1778 

i793 

1808 

1823  i838 

17 

42 

7032 

7046 

7060 

7075 

7089 

7104 

17 

43 

i853 

1868 

i883 

1897 

1912  1927 

16 

43 

7118 

7l32 

7147 

7161 

7i75 

7i9o 

16 

44 

1942 

1957 

1972 

1987 

2OO2  2017 

i5 

44 

7204 

7218 

7233 

7247 

7261 

7276 

i5 

45 

2031 

2046 

2061 

2076 

2091  2IO6 

i4 

45 

7290 

73o4 

73i9 

7333 

7347 

7362 

i4 

46 

2121 

2i36 

2i5o 

2i65 

2l8o  2195 

i3 

46 

7376 

739o 

74o5 

7419 

7433 

7448 

i3 

47 

22IO 

2225  224O 

2255 

2269  2284 

12 

47 

7462 

7476 

7491 

75o5 

75i97534 

12 

48 

2299 

23i4 

2329 

2344 

2358  2373 

II 

48 

7548  7562 

7576759i 

76o5:76i9 

II 

49 

2388 

24o3  2418 

2433 

2448  2462 

10 

49 

7634  7648 

7662  7677 

-7691  77o5 

IO 

5o 

9.912477 

2492  2507 

2522 

2537255i 

9 

5o 

9.9177197734 

7748  7762 

7777  7791 

9 

5i 

2566 

258i 

2596 

26l  I 

2625  2640 

8 

5i 

7805  7819 

7834  7848 

7862  7877 

8 

52 

2655 

2670  2685 

2700 

2-714  2-729 

7 

52 

7891  79o5 

7919  7934 

7 

53 

2744 

2759 

2774 

2788 

28o3  2818 

6 

53 

7976  7991  8oo5  8019 

8o338o48 

6 

54 

2833 

2848 

2862 

2877 

2892  290-7  5 

54 

806280768090810581198133  5 

55 

2922 

29362951 

29662981  2995  4 

55 

814781628176819082048219  4 

56 

3*oio 

3o25 

3o4o3o55j3o693o84  3 

56 

82338247:8261827682908304  3 

5? 

3099 

3n4 

3i283i43:3i583i73  2 

57 

83i8'83338347836i  83758389  2 

58 

3i87 

32O2 

32173232  32473261 

i 

58 

84o4  84i8  8432  8446  846i  8475  i 

59 

3276 

3291 

33o6332o!3335335o  o 

59 

8489  85o385i7  8532  8546856o  o 

60" 

50" 

40"   30"   20"   10"  .  ^ 

60"     50"  t  40"   30"   20"   107   ^ 

Co-sine  of  35  Degrees.     i 

Co-sine  of  34  Degrees.     ^ 

T.PartM'  2/  3"  4"  5//  6//  7*  8//  9"-  •''  P  P^n"  2//  3//  4//  5"  6"  7"  8"  9" 

J  2   3   5 

6   8   9  11  12  14  ;     "^  1   3   4   6   7   9  10  12  13 

LOGARITHMIC    TANGENTS, 


d  1    Tangent  of  54  Degrees. 

a 

Tangent  of  55  Degrees. 

* 

0" 

10" 

20" 

30" 

40"  1  50" 

* 

0" 

10" 

20" 

30"  |  40" 

\5(y 

0 

io.i38739 

8783 

8828 

8872 

89i6 

896o 

5o 

o 

10.154773 

48i8 

4863 

49o8 

4952 

4997 

v 

i 

9oo5j9o49 

9o93 

9i38 

9l82 

9226 

58 

I 

5042 

5o87 

5i32 

5i77 

5221 

5266 

58 

2 

9270 

93i5 

9359 

94o3 

9448 

9492 

57 

2 

53n 

5356 

54oi 

5446 

5490 

5535 

57 

3 

9536 

958o 

9625 

9669 

97l3 

9758 

56 

3 

558o 

56255670 

57i5 

5759 

58o4 

5b 

4 

98o2 

9846 

989i 

9935 

9979 

..24 

55 

4 

5849 

5894  5939 

5984 

6o29 

6o73 

55 

5 

10.  i4oo68 

01  12 

oi57 

0201 

0245 

0290 

54 

5 

6118 

6i6362o8 

6253 

6298 

6343 

54 

6 

o334 

o378 

0423 

o467 

o5ii 

o556 

53 

6 

6388 

6432  6477 

6522 

6567 

6612 

53 

7 

0600 

o644 

o689 

0733 

0777 

0822 

52 

7 

6657 

6-702 

6747 

679i 

6836 

688  1 

52 

8 

0866 

o9io 

o955 

0999 

io43 

1088 

5i 

8 

6926 

697i 

7oi6 

7o6i 

7106 

7i5i 

5i 

9 

Il32 

1  176 

1221 

1265 

i3o9 

i354 

5o 

9 

7i95 

-7240 

7285 

733o 

7375 

74?o 

5o 

10 

io.i4i398 

1442 

i487 

i53i 

i576 

1620 

49 

10 

io.i57465 

75io 

7555 

76oo 

7645 

7689 

49 

ii 

1  664 

r7°9 

i753 

1797 

1842 

1886 

48 

ii 

7734 

7779 

•7824 

7869 

79i4 

7959 

48 

12 

I93i 

i975 

2019 

2064 

2108 

2l52 

47 

19 

8oo4 

8049 

8o94 

8i39 

8i84 

8229 

47 

i3 

2I97 

2241 

2286 

233o 

2374 

24l9 

46 

r3 

8273 

83i8 

8363 

84o8 

8453 

8498 

46 

i4 

2463 

25o8 

2552 

2596 

2641 

2685 

45 

i4 

8543 

8588 

8633 

8678 

8723 

8768 

45 

i5 

2780 

2774 

2818 

2863 

2907 

2952 

44 

ID 

88i3 

8858 

89o3 

8948 

8993 

9o38 

44 

16 

2996J3o4i 

3o85 

3i29 

3i74 

3218 

43 

16 

9o83 

9I28 

9i73 

92l8 

9263 

93o7 

43 

17 

3263 

33o7 

335i 

3396 

344o 

3485. 

42 

i7 

9352 

9397 

9487 

9532 

9577 

42 

18 

3529 

3574 

36i8 

3662 

3707 

375i 

4r 

18 

9622 

9667 

97I2 

9757 

98o2 

9847 

4i 

19 

3796 

384o 

3885 

3929 

3974 

4oi8 

4o 

19 

9892 

9937 

9982 

..27 

..72 

.n7 

4o 

20 

10.  144062 

4io7 

4i5i 

4i96 

4240 

4285 

39 

20 

10.  160162 

0207 

0252 

0297 

0342 

o387 

39 

21 

4329 

4374 

44i8 

4463 

4507 

455i 

38 

21 

0432 

o477 

0522 

o567 

0612 

o657 

38 

22 

4596 

464o 

4685 

4729 

4774 

4818 

37 

22 

0703 

o748 

o793 

o838 

o883 

0928 

37 

23 

4863 

49o7 

4952 

4996 

5o4i 

5o85 

36 

23 

0973 

1018 

io63 

1108 

n53 

n98 

36 

24 

5i3o 

52  1  9 

5263 

53o8 

5352 

35 

24 

1243 

1288 

i333 

i378 

1423 

i468 

35 

25 

5397 

544i 

5486 

553o 

5575 

5619 

34 

25 

i5i3 

i558 

i6o3 

1  648 

i693 

I739 

34 

26 

5664 

57o8 

5753 

5797 

5842 

5886 

33 

26 

1784 

l829 

i874 

1919 

i964 

2O09 

33 

27 

593i 

5975 

DO2O 

6o64 

6io9 

6i53 

32 

27 

2o54 

2099 

2i44 

2i89 

2234 

2279 

32 

28 

6i98 

6242 

628-7 

633i 

6876 

6420 

3i 

28 

2325 

2370 

24i5 

2460 

25o5 

2550 

3i 

29 

6465 

65o9 

6554 

6598 

6643 

668-7 

3o 

29 

2595 

2640 

2685 

2730 

2775 

2821 

3o 

3o 

10.146732 

6777 

6821 

6866 

69io 

6955 

29 

3o 

10.  162866 

29II 

2956 

3ooi 

3o46 

3o9i 

29 

3i 

6999 

7o44 

7o88 

7i33 

7177 

7222 

28 

3i 

3i36 

3i8i 

3227 

3272 

33i7 

3362 

28 

32 

7267 

73n 

7356 

74oo 

7445 

7489 

27 

32 

34o7 

3452 

3497 

3542 

3588 

3633 

27 

33 

7534 

7578 

7623 

7668 

7712 

7757 

26 

33 

3678 

3723 

3768 

38i3 

3858 

39o4 

26 

34 

7801 

7846 

789o 

7935 

798o 

8024 

25 

34 

3949 

3994 

4o39 

4o84 

4l29 

4i74 

25 

35 

8o69 

8n3 

8i58 

82o3 

8292 

24 

35 

4220 

4265 

43io 

4355 

44oo 

4445 

24 

36 

8336 

838i 

8425 

847o 

85i5 

8559 

23 

36 

449i 

4536 

458i 

4626 

467i 

47i6 

23 

'37 

86o4 

8648 

8693 

8738 

8782 

8827 

22 

37 

4762 

48o7 

4852 

4897 

4942 

4988 

22 

38 

8871 

89i6 

896i 

9oo5 

9o5o 

9095 

21 

38 

5b33 

5o78 

5i23 

5i68 

52i3 

5259 

21 

39 

9i39 

9i84 

9228 

9273 

93i8 

9362 

20 

39 

53o4 

5349 

5394 

5439 

5485 

553o 

20 

4o 

9452 

9496 

954i 

9585 

963o 

19 

4o 

IO.  165575 

5620 

5666 

5711 

5756 

58oi 

19 

4i 

9675 

97i9 

9764 

98o9 

9853 

9898 

18 

4i 

5846 

5892 

5937 

5982 

6027 

6o73 

18 

42 

9943 

9987 

..32 

..76 

.121 

.166 

17 

42 

6118 

6i63 

62b8 

6253 

6299 

6344 

17 

43 

IO.  I5O2IO 

0255 

o3oo 

o344 

o389 

o434 

16 

43 

6389 

6434 

648o 

6525 

657o 

66i5 

16 

44 

0478 

o523 

o568 

0612 

o657 

0702 

i5 

44 

6661 

6706 

675i 

6796 

6842 

6887 

i5 

45 

0746 

o79i 

o836 

0880 

092!) 

0970 

i4 

45 

6932 

6977 

7023 

7068 

7ii3 

7i58 

i4 

46 

ioi4 

io59 

no4 

n49 

ii93 

1238 

i3 

46 

7204 

7249 

7294 

7340 

7385 

743o 

i3 

47 

1283 

l327 

1872 

i4i7 

i46i 

i5o6 

12 

47 

7475 

752I 

7566 

7611 

7657 

7702 

12 

48 

i55i 

i595 

i64o 

i685 

1780 

1774 

II 

48 

7747 

7792 

7838 

7883 

7928 

7974 

II 

49 

i8i9 

i864 

i9o8 

i953 

i998 

2043 

10 

49 

8oi9 

8o64 

8io9 

8i55 

8200 

8245 

10 

5o 

10.  152087 

2l32 

2177 

2221 

2266 

23ll 

9 

5o 

io.i6829i 

8336 

838i 

8427 

8472 

85i7 

9 

5i 

2356 

2400 

2445 

2/QO 

2535 

2579 

8 

5i 

8563 

8608 

8653 

8699 

8744 

8789 

8 

52 

2624 

2669 

2713 

2758 

28o3 

2848 

7 

52 

8835 

8880 

8925 

897i 

9oi6 

9061 

7 

53 

2892 

2937 

2982 

3027 

3o7i 

3n6 

6 

53 

9107 

9l52 

9i97 

9243 

9288 

9333 

6 

54 

3i6i 

3206 

325o 

3295 

334o 

3385 

5 

54 

9379 

94a4 

9469 

95i5 

956o 

9605 

5 

55 

343o 

3474 

35i9 

3564 

36o9 

3653 

4 

55 

965i 

9696 

9742 

9787 

9832 

9878 

4 

56 

3698 

3743 

3788 

3832 

3877 

3922 

3 

56 

9923 

9968 

..59 

.io5 

.i5o 

3 

57 

3967 

4OI2 

4o56 

4ioi 

4i46 

4191 

2 

57 

io.i7oi95 

0241 

0286 

o33i 

o377 

0422 

2 

58 

4236 

4280 

4325 

4370 

44i5 

446o 

I 

58 

o468 

o5i3 

o558 

o6o4 

o649 

0695 

I 

59 

45o4 

4549 

4594 

4639 

4684 

4728 

O 

59 

o74o 

o785 

o83i 

0876 

0922 

0967 

O 

60" 

50" 

40" 

30" 

20" 

10" 

d 

60" 

50" 

40" 

30" 

20" 

10" 

c 

Co-tangent  of  35  Degrees. 

* 

Co-tangent  of  34  Degrees. 

3 

p  p  .  <  1"  2"  3"  4"  5"  6"  7"  8"  9" 
I  4   9  13  18  22  27  31  36  40 

P.  Part  J  5  "g  14  ig  23  27  32  36  41 

LOGARITHMIC    SINES. 


A 

Sine  of  56  Degrees. 

c 

IS 

Sine  of  57  Degrees. 

2 

0" 

10" 

20" 

30" 

40"   50" 

s 

0" 

10" 

20" 

30" 

40" 

50" 

o 

9.918574 

8588 

86o3 

8617 

863i  8645 

59 

0 

9.92359i 

36o5 

36i9 

3632 

3646 

366o 

59 

i 

8659J8674 

8688 

8702 

8716 

873o 

58 

I 

3673 

3687 

37oi 

37i4 

3728 

3742 

58 

2 

8745 

8759 

8773 

8787 

8801 

88i5 

57 

2 

3755 

3769 

3783 

3796 

38io 

3824J57 

! 

883o 

8844 

8858 

8872 

8886 

8900 

56 

3 

3837 

385i 

3865 

3878 

3892 

39o6!56 

4 

89i5 
9000 

8929 
9012 

8943 

9O28 

8957 

9042 

897i  8985 
9o56  9070 

55 

54 

L 

r. 

39i9 
4ooi 

3933 
4oi5 

3946 
4028 

396o 
4042 

3974 
4o55 

3987 
4o69 

r  r 

j  -j  i 

54 

6 

9o85 

9099 

9n3 

9I2? 

9i4i 

9i55 

53 

6 

4o83 

4o96 

4no 

4124 

4i37 

4i5i 

53 

7 

9169 

9184 

9i98 

92I2 

9226^9240 

52 

1 

4i64 

4178 

4l92 

42o5 

42I9 

4232 

52 

8 

9254 

9268 

9282  9297 

93u  9325 

5i 

8 

4246 

4260 

4273 

4287 

43oo 

43i4 

5i 

9 

9339 

9353 

9367938i 

939594io 

5o 

9 

4328 

434i 

4355 

4368 

4382 

4396 

5o 

10 

9.919424 

9438 

9452  9466 

9480  9494 

49 

10 

9.9244o9 

4423 

4436 

445o 

4464 

4477 

49 

ii 

95o8 

9522 

9537 

955i 

9565  9579 

48 

ii 

449i 

45o4 

45i8 

453i 

4545 

4559 

48 

12 

ivi 

9593 
9677 

9607 

9692 

962I 

97o6 

9635 

9720 

9649  9663 
97349748 

47 
46 

12 

i3 

4572 
4654 

4586 
4667 

4599 
468  1 

46i3 
4694 

4626 
47o8 

464o 
4721 

47 

46 

iZ 

9762 

9776 

979° 

•9804 

9818 

9832 

45 

i4 

4735 

4748 

4762 

4776 

4789 

48o3 

45 

j  t 

9846 

9860 

9875 

9889 

9903 

9917 

44 

i5 

48i6 

483o 

4843 

4857 

487o 

4884 

44 

16 

993i 

9945 

9959 

9973 

9987 

...  i 

43 

16 

4897 

49" 

4924 

4938 

4952 

4965 

43 

17 

9.920015 

0029 

oo43 

oo57 

0071 

oo85 

42 

"7 

4979 

4992 

5oo6 

5oi9 

5o33 

5o46 

42 

18 

0099 

OIlS 

0127 

oi4i 

oi56 

OI70 

4i 

18 

5o6o 

5073 

5o87 

5  1  oo 

5n4 

5127 

4i 

19 

0182 

0198 

O2I2 

0226 

0240 

O25^ 

4o 

I9 

5i4i 

5i54 

5i68 

5i8i 

5i95 

5208 

4o 

20 

9.920268 

0282 

O296 

o3io 

0324 

o338 

39 

20 

9.925222 

5235 

5249 

5262 

5276 

5289 

39 

21 

o352 

o366 

o38o 

o394 

o4o8 

0422 

38 

21 

53o3 

53i6 

533o 

5343 

5357 

537o 

38 

22 

o436 

o45o 

o464 

o478 

0492 

o5o6 

37 

22 

5384 

5397 

54n 

5424 

5438 

545i 

37 

23 

O520 

o534 

o548 

o562 

o576 

oSgo 

36 

23 

5465 

5478 

5491 

55o5 

55i8 

5532 

36 

24 

o6o/! 

0618 

o632 

o646 

0660 

o674 

35 

24 

5545 

5559 

5572 

5586 

5599 

56i3 

35 

25 

0688 

0702 

07160730 

o744 

o758 

34 

25 

5626 

564o 

5653 

5667 

568o 

5693 

34 

26 

0772 

0786 

o8oo|o8i4 

0828 

0842 

33 

26 

57°7 

5720 

5734 

5747 

576i 

5774 

33 

27 

o856 

0869 

o883 

0897 

0911 

0925 

32 

27 

5788 

58oi 

58i4 

5828 

584i 

5855 

32 

28 

o939 

o953 

o967 

0981 

o995 

1009 

3i 

28 

5868 

5882 

5895 

59o8 

5922 

5935 

3i 

29 

IO22 

1037 

io5i 

io65 

1079 

1093 

3o 

29 

5949 

5962 

5976 

5989 

6OO2 

6016 

3o 

3o 

9.921107 

II2I 

n34 

n48 

1162 

n76 

29 

3o 

9.926O29 

6o43 

6o56 

6o69 

6o83 

6096 

29 

3r 

1190 

1204 

1218 

1232 

I246 

1260 

28 

3i 

6110 

6i23 

6i36 

6i5o 

6x63 

6177 

28 

32 

1274 

1288 

1302 

i3i5 

I329 

1  343 

27 

32 

6i9o 

62o3 

621-7 

623o 

6244 

6257 

27 

33 

i357 

l37I 

i385 

i399 

i4i3 

l427 

26 

33 

6270 

6284 

6297 

63ii 

6324 

6337 

26 

34 

i44i 

i455 

1  468 

1482 

1496 

i5io 

25 

34 

635i 

6364 

6377 

639i 

64o4 

64i8 

25 

35 

i524 

i538 

i552 

i566 

i58o 

i593 

24 

35 

643i 

6444 

6458 

647i 

6484 

6498 

24 

36 

1607 

1621 

i635 

i649 

i663 

1677 

23 

36 

65u 

6525 

6538 

655i 

6565 

6578 

23 

3? 

1691 

1704 

1718 

1732 

1746 

1760 

22 

3  '7 

659i 

66o5 

6618 

663i 

6645 

6658 

22 

38 

1  774 

1788 

1802 

i8i5  i829 

i843 

21 

38 

667i 

6685 

6698 

67n 

6725 

6738 

21 

39 

1857 

1871 

i885 

i899  i9i2 

1926 

2O 

39 

675i 

6765 

6778 

679i 

68o5 

6818 

20 

4o 

9.921940 

1954 

i968 

198211995 

2009 

J9 

4o 

9.  926831 

6845 

6858 

687i 

6885 

6898 

X9 

4i 

2023 

2037 

2o5i 

2o65  2079 

2092 

18 

4i 

69u 

6925 

6938 

695i 

6965 

6978 

18 

42 

2106 

2I2O 

2i34 

2148 

2162 

2I75 

'7 

42 

6991 

7oo5 

7018 

7o3i 

7o44 

7o58 

17 

43 

2189 

2203 

2217 

223l 

2244 

2258 

16 

43 

707: 

7o84 

7o98 

7in 

7I24 

7i38 

16 

44 
45 

2272 
2355 

2286 

2369 

23oo 

2383 

23i3  2327 
239624io 

234i 
2424 

i5 

i4 

44 
45 

7i5i 
7231 

7164 
7244 

7177 

7257 

7i9i 

7270 

7204 

7284 

72I7 
7297 

i5 

i4 

46 

2438 

2452 

2465 

2479  2493 

2507 

i3 

46 

73io 

7324 

7337 

735o 

7363 

7377 

i3 

47 

2520 

2534 

2548 

2562  2576 

2589 

12 

47 

739o 

74o3 

74i6 

743o 

7443 

7456 

12 

48 

26o3 

2617 

263i 

2644  2658 

2672 

II 

48 

747o 

7483 

7496 

75o9 

7523 

7536 

II 

49 

2686 

2700 

2?I3 

2727  2741 

2755 

IO 

49 

7549 

7562 

7576 

7589 

•7602 

76i5  10 

5o 

9.922768 

2782 

2796 

28102823 

2837 

9 

5o 

9.927629 

7642 

7655 

7668 

768i 

7695 

9 

5i 

285i 

2865 

2878 

2892  29O6 

2920 

8 

5i 

77o8 

772i 

7734 

7748 

776i 

7774 

8 

52 

2933 

2947 

296i 

2975  2988 

3002 

7 

52 

7787 

78oi 

7814 

7827 

784o 

7853 

7 

53 

3oi6 

3o3o 

3o43 

3o57  3071 

3o84 

6 

53 

7867 

788o 

7«93 

7906 

7920 

7933 

6 

54 

3o98 

3lI2 

3i26 

3i393i53 

3167 

5 

54 

7946 

7959 

7972 

7986 

7999 

8012 

5 

55 

3i8i 

3ig4 

3208 

3222  3235 

3249 

4 

55 

8o25 

8o38 

8o52 

8o65 

8o78 

8o9i 

4 

56 

3263 

3277 

329O 

33o433i8 

333i 

3 

56 

8io4 

8118 

8i3! 

8i448i57 

8i7o 

3 

57 

3345 

3359 

3372 

338634oo 

34i4 

2 

57 

8i838i97 

8210 

8223J8236 

8249 

2 

58 

3427 

344  1 

3455 

34£8j3482 

3496 

I 

58 

8263  8276 

8289 

83o283i5 

8828  i 

59 

35o9 

3523 

3537 

355o  3564 

3578 

O 

59 

834s 

8355 

8368 

838i  839484o7i  o 

60" 

50" 

40" 

30"   20" 

10" 

d 

60" 

50" 

40" 

30"   20"   10" 

e 

Co-sine  of  33  Degrees. 

§ 

Co-sine  of  32  Degrees. 

1 

.$1"  2"  3"  4"  5"  6"  7"  8"  9" 

P  Pnrt5  1/  ~"  3//   4//   5"   6"  7"   8"   9" 

irt}  1   3   4  6   7   8  10  11  13 

r.ranj  i   3   4   5   7   8   9  n  12 

LOGARITHMIC    TANGENTS. 


8) 


A 

Tangent  of  56  Degrees. 

.3 

Tangent  of  57  Degrees. 

ji 

0" 

10" 

20" 

30" 

40"  |  50" 

n 

0" 

10" 

20" 

30"  |  40"  |  50" 

o 

10.  171013 

io58 

no3 

1149 

1194 

I24o 

59 

0 

10.187483 

7529 

7575 

7621 

7667 

7713 

59 

I 

1285 

i33i 

i376 

1421 

i467 

l5l2 

58 

i 

7759 

78o5 

785i 

7898 

7944 

799° 

58 

2 

i558 

i6o3 

i649 

1694 

i739 

i785 

57 

2 

8o36 

8082 

8128 

8174 

82208267 

5? 

3 

i83o 

i876 

I92I 

J967 

2OI2 

ao58 

56 

3 

83i3 

8359 

84o5 

845  1 

8497 

8543 

56 

4 

2103 

2149 

2I94 

2239 

2285 

233o 

55 

4 

859o 

8636 

8682 

8728 

8774 

8820 

55 

5 

2376 

2421 

2467 

25l2 

2558 

26o3 

54 

5 

8866 

89i3 

8959 

9005 

9o5i 

9097 

54 

6 

2649 

2694 

274o 

2785 

283i 

28-76 

53 

6 

9i43 

9190 

9236 

9282 

9328 

9374 

53 

7 

2922 

2967 

3oi3 

3o58 

3io4 

3i49 

52 

7 

9420 

9467 

95i3 

9559 

96o5 

965i 

52 

8 

3i95 

324o 

3286 

333i 

3377 

3422 

5i 

8 

9698 

9744 

9-790 

9836 

9882 

9929 

5i 

9 

3468 

35i3 

3559 

36o4 

365o 

3695 

5o 

9 

9975 

.  .21 

..67 

.n3 

.160 

.206 

5o 

10 

10.  173741 

3786 

3832 

3877 

3923 

3968 

49 

10 

10.  190252 

0298 

o344 

0391 

o437 

o483 

49 

ii 

4oi4 

4o6o 

4io5 

4i5i 

4196 

4242 

48 

1  1 

0529 

o576 

0622 

0668 

o7i4 

0760 

48 

12 

4287 

4333 

4378 

4424 

4469 

45i5 

47 

12 

0807 

o853 

0899 

o945 

0992 

io38 

47 

i3 

456i 

46o6 

4652 

4697 

4743 

4788 

46 

i3 

io84 

n3o 

1177 

1223 

1269 

i3i5 

46 

i4 

4834 

488o 

4925 

497i 

5oi6 

5o62 

45 

i4 

i362 

i4o8 

i454 

i5oi 

1  547 

i593 

45 

i5 

5107 

5i53 

5i99 

5244 

5290 

5335 

44 

i5 

i639 

1686 

I732 

1778 

1824  i87i 

44 

16 

538i 

5427 

5472 

55i8 

5563 

56o9 

43 

16 

1917 

i963 

2010 

2o56 

2102 

2l49 

43 

17 

5655 

57oo 

5746 

579i 

5837 

5883 

42 

17 

2195 

224l 

2287 

2334 

238o 

2426 

42 

18 

5928 

5974 

6oi9 

6o65 

6m 

6i56 

4i 

18 

24?3 

2519 

2565 

2612 

2658;27o4 

4i 

19 

6202 

6247 

6293 

6339 

6384 

643o 

4o 

*9 

2751 

2797 

2843 

2890 

2936  2982 

4o 

20 

10.176476 

652i 

6567 

66i3 

6658 

67o4 

39 

20 

10.  193029 

3075 

3l2I 

3i68 

32l4 

3260 

39 

21 

6749 

6795 

684  1 

6886 

6932 

6978 

38 

21 

3307 

3353 

3399 

3446 

3492 

3538 

38 

22 
23 

7023 

7297 

7o69 

7343 

7n5 
7389 

-7160 

7434 

7206 

748o 

7252 
7526 

3? 
36 

22 
23 

3585 
3863 

363i 
3909 

3678 
3956 

3724 

40O2 

377o38i7 
4o494o95 

37 
36 

24 

757i 

76l7 

7663 

77o8 

7754 

7800 

35 

24 

4i4i 

4i88 

4234 

4281 

4327 

4373 

35 

25 

7846 

789i 

7937 

7983 

8028 

8074 

34 

25 

4420 

4466 

45i3 

4559 

46o5 

4652 

34 

26 

8120 

8i65 

8211 

8257 

83o3 

8348 

33 

26 

4698 

4?45 

4791 

4837 

4884 

493o 

33 

27 

8394 

844o 

8485 

853i 

8577 

8623 

32 

27 

4977 

5o23 

5070 

5n6 

5i62 

5209 

32 

28 

8668 

87i4 

876o 

88o5 

885i 

8897 

3i 

28 

5255 

53o2 

5348 

5395 

544  1 

5487 

3i 

29 

8943 

8988 

9034 

9o8o 

9126 

9171 

3o 

29 

5534 

558o 

5627 

5673 

5720 

5766 

3o 

3o 

IO.  I792I7 

9263 

93o9 

9354 

9400 

9446 

29 

3o 

IO.  I958l3 

5859 

5906 

5952 

5999 

6o45 

29 

3i 

9492 

9537 

9583 

9629 

9675 

9720 

28 

3i 

6091 

6i38 

6i84 

&23l 

6277 

6324 

zS 

32 

9766 

9812 

9858 

99o4 

9949 

9995 

27 

32 

6370 

6417 

6463 

65io 

655666o3 

27 

33 

10.  i8oo4i 

008-7 

Ol32 

01-78 

0224 

0270 

26 

33 

6649 

6696 

6742 

6789 

6835  6882 

26 

34 

o3i6 

o36i 

o4o7 

o453 

o499 

o545 

25 

34 

6928 

6975 

7021 

7068 

7n4  7161 

25 

35 

0590 

o636 

0682 

0728 

o774 

0819 

24 

35 

7208 

7254 

73oi 

7347 

739417440 

24 

36 

o865 

0911 

o957 

ioo3 

io48 

1094 

23 

36 

7487 

7533 

758o 

7626 

76737719 

23 

37 

n4o 

1186 

1232 

I278 

i323 

1  369 

22 

37 

7766 

78i3 

7859 

7906 

7952  7999 

22 

38 

i4i5 

i46i 

i5o7 

i553 

i598 

1  644 

21 

38 

8o45 

8092 

8i38 

8i85 

8232 

8278 

21 

39 

1690 

i736 

I782 

1828 

i874 

1919 

20 

39 

8325 

8371 

84i8 

8465 

85n 

8558 

2O 

4o 

10.  181965 

2OII 

2o57 

2103 

2l49 

2195 

I9 

4o 

10.  198604 

865i 

8697 

8744 

879i 

8837 

19 

4i 

2241 

2286 

2332 

2378 

2424 

2470 

18 

4i 

8884 

893o 

8977 

9024 

9o7o 

9n7 

18 

42 

25i6 

2562 

2608 

2653 

2699 

2745 

17 

42 

9164 

9210 

9257 

93o3 

935o 

9397 

17 

43 

279I 

2837 

2883 

2929 

2975 

3021 

16 

43 

9443 

9490 

9537 

9583 

963o 

16 

44 

3o67 

3lI2 

3i58 

325o 

3296 

i5 

44 

9723 

9770 

98i6 

9863 

99io 

9956 

i5 

45 

3342 

3388 

3434 

348o 

3526 

3572 

i4 

45 

IO.2OOOO3 

oo5o 

oo96 

oi43 

0190 

0236 

i4 

46 

36i8 

3664 

3-709 

3755 

38oi 

3847 

i3 

46 

0283 

o33o 

o376 

0423 

0470 

o5i6 

i3 

47 

3893 

3939 

3985 

4o3i 

4o77 

4i23 

12 

47 

o563 

0610 

o656 

0703 

0780 

0796 

12 

48 

4169 

42i5 

4261 

43o7 

4353 

4399 

II 

48 

o843 

0890 

o937 

o983 

io3o 

1077 

II 

49 

4445 

4491 

4537 

4583 

4629 

4674 

10 

49 

1123 

1170 

I2I7 

1263 

i3io 

i357 

10 

5o 

IO.  l8472O 

4766 

4812 

4858 

49o4 

495o 

9 

5o 

I0.20l4o4 

i45o 

i497 

1  544 

i59i  i637 

9 

5i 

4996 

5o42 

5o88 

5i34 

5i8o 

5226 

8 

5i 

1  684 

1731 

I777 

1824 

1871  1918 

8 

52 

5272 

53i8 

5364 

54io 

5456 

55o2 

7 

52 

1964 

2OII 

2o58 

2io5 

2i5i  2198 

7 

53 

5548 

5594 

564o 

5686 

5732 

5778 

6 

53 

2245 

2292 

2338 

2385 

2432  2479 

6 

54 

5824 

587i 

591-7 

5963 

6oo9 

6o55 

5 

54 

2526 

2572 

26l9 

2666 

2713  2759 

5 

55 

6101 

6i47 

6193 

6239 

6285633i 

4 

55 

2806 

2853 

2900 

2947 

2993|3o4o 

4 

56 

6377 

6423 

6469 

65i5 

656i  66o7 

3 

56 

3087 

3i34 

3i8i 

3227 

3274332i 

3 

57 

6653 

6699 

6745 

679i 

6837 

6884 

2 

5? 

3368 

34i5 

346i 

35o8 

35553602 

2 

58 

6930 

6976 

7O22 

7o68 

7114 

7160 

I 

58 

3649 

3696 

3742 

3789 

3836|3883 

I 

59 

7206 

7252 

7298 

7344 

739o 

7437 

0 

59 

393o 

3977 

4023 

4070 

4ii74i64 

O 

60" 

50" 

40" 

30" 

20"   10" 

j 

60"      50" 

40" 

30" 

20"   10" 

j 

Co-tangent  of  33  Degrees. 

§ 

Co-tangent  of  32  Degrees. 

§ 

P  P  t$  l"  2"  3//  4"  5"  6//  7"  8"  9" 

(1"  2"  3"  4"  5"  6"  7"  S"  9" 

I  5   9  14  18  23  27  32  37  41 

'  art{  5   9  14  19  23  28  33  37  42 

LOGARITHMIC    SINES. 


1 

.a 

Sine  of  58  Degrees. 

c 

Sine  of  59  Degrees. 

9 

0"    [  10" 

20"   30" 

40" 

f50" 

• 

0"     10" 

20" 

30" 

40" 

50" 

0 

9.928420(8434 

8447  8460,8473 

8486  59 

0,9.  933o66;3o78 

3o9i 

3io4 

3n6 

3129 

5o 

I 

8499  85i3;85268539  8552 

856558 

I 

3i4i  3i54 

3i67 

3i79 

3192 

32o5  58 

2 

8578  8591 

86o586i8863i 

8644  57 

2 

32i7323o 

3243 

3255 

3268 

328o  57 

3 
4 

8657  867o;8683  8696  87io 
87868749  8762  8775  8788 

8723j56 

8801  55 

3 

4 

3293|33o6 
3369338i 

33i8 
3394 

333i 

34o7 

3344 
3419 

3356 
3432 

56 
55 

5 

88i5i8828884i  8854 

8867 

888o;54 

5 

3445 

3457 

347o 

3482 

3495 

35o8 

54 

6 

8893  8906  8919  8933  8946  SgSg  53 

6 

3520 

3533 

3545 

3558 

357i 

3583 

53 

7 

8972 

8985  8998  9011 

9024  9o37  52 

7 

3596 

36o8 

362i 

3633 

3646 

3659 

52 

8 
9 

9129 

9063  9077  9090  9  103:911  6'  5  1 
9142  9i55  9168  9181  9194150 

8 
9 

367i 
3747 

3684 
3759 

3696 
3772 

37o9 

3784 

3722 
3797 

3734 
38io 

5i 

5o 

10 

9.929207 

9220  9233  924^9260  9273149 

10 

9.933822 

3835 

3847 

386o 

3872 

3885 

49 

ii 

9286 

9299  9312  9325  9338 

935i48 

ii 

3898(3910 

3923 

3935 

3948 

3960 

48 

12 

9364 

9377  9390  9403  9416  9429^7 

12 

3973 

3985 

3998 

4on 

4o23 

4o36 

47 

i3 

9442 

9455  9468  9482  9495 

95o846 

i3 

4o48 

4o6i 

4o73 

4o86 

4o98 

4in 

46 

i4 

9521 

9534  95479560  9573 

9586!45 

i4 

4l23 

4i36 

4i48 

4i6i 

4i74 

4i86 

45 

i5 

9599 

9612  962596389651 

9664  44 

i5 

4199 

4211 

4224 

4236 

4249 

4261 

44 

16 

9677 

9690  9703  9716  9729 

9742J43 

16 

4274 

4286 

4299 

43n 

4324 

4336 

43 

'7 

9755 

9768  9781  97949807 

9820  42 

17 

4349 

436i 

4374 

4386 

4399 

44" 

42 

18 

9833 

9846  9859^9872  9885 

o8o84i 

18 

4424 

4436 

4449 

446  1 

4474 

4486 

4i 

19 

9911 

9924 

99379950 

9963997640 

'9 

4499 

45u 

4524 

4536 

4549 

456i 

4o 

20 

9.929989 

.  .  .2 

..i5  ..28 

.  .41 

..5439 

20 

9-934574 

4586 

4599 

46n 

4624 

4636 

39 

21 

9.930067 

0080  0093  0106  oi  19 

oi32'38 

21 

4649 

466i 

4674 

4686 

4699 

4711 

38 

22 

oi45 

oi58  0171  oi84 

0197  0210)37 

22 

4723 

4736 

4748 

4761 

4773 

4786 

37 

23 

O223 

O236  0249  °262 

0274  0287  36 

23 

4798 

48n 

4823 

4836 

4848 

486i 

36 

24 
25 

o3oo 
o378 

o3i3  0326  0339 
0391  04040417 

o352!o365 
o43oo443 

35 
34 

24 
25 

4873 
4948 

4885 
496o 

4898 
4973 

4910 
4985 

4923 

4997 

4935 
5oio 

35 
34 

26 

o456 

0469  0482  0495  0507  o52O 

33 

26 

5O22 

5o35 

5o47 

5o6o 

5072 

5o84 

33 

27 
28 
29 

o533 
06  1  1 
0688 

o546  0559  °572  °585  ©598 
0624  o637|o65o!o663jo675 
0701  0714  0727  0740  0753 

32 

3i 
3o 

27 
28 
29 

5<>97 
5i7i 
5246 

5io9 
5i84 
5258 

5l22 

5i96 

527I 

5i34 
5209 
5283 

5i47 

5221 
5296 

5i59 
5234 
53o8 

32 

3i 
3o 

3o 

0.930766 

07790792 

o8o4o8i7'o83o 

29 

3o 

9.93532o 

5333 

5345 

5358 

537o 

5382 

29 

3i 

o843 

o856  0869 

0882 

o895 

0908 

28 

3i 

5395 

54o7 

5420 

5432 

5444 

5457 

28 

32 

0921 

0933  0946 

o959 

o972 

0985 

27 

32 

5469 

5482 

5494 

55o6 

55i9 

553i 

27 

33 

0998 

101  I 

1024 

io36 

io49 

1062 

26 

33 

5543 

5556 

5568 

558i 

5593 

56o5 

26 

34 

1075 

1088 

IIOI 

in4 

1127 

1  1  39 

25 

34 

56i8 

563o 

5642 

5655 

5667 

5679 

25 

35 

1x5* 

n65 

1178 

1191 

I2O4 

1217 

24 

35 

5692 

57o4 

57i7 

5729 

5741 

5754 

24 

36 

1229 

1242 

1255 

1268 

1281 

1294 

23 

36 

5766 

5778 

579i 

58o3 

58i5 

5828 

23 

37 

i3o6 

i3i9 

i332 

1  345 

i358 

1371 

22 

37 

584o 

5852 

5865 

5877 

5889 

5902 

22 

38 

1383 

i396 

1409 

l422 

i435 

1  448 

21 

38 

59i4 

5926 

5939 

595i 

5963 

5976 

21 

39 

i46o 

i473 

i486 

1499 

I5l2 

i525 

2O 

39 

5988 

6000 

6oi3 

6o25 

6o37 

6o5o 

2O 

4o 

9.93i537 

i55o 

i563 

i576 

i589 

1601 

'9 

4o 

9.936o62 

6o74 

6o87 

6099 

61  1  1 

6124 

»9 

4i 

1614 

1627 

i64o 

i653 

1666 

1678 

18 

4i 

6i36 

6i48 

6161 

6i73 

6i85  6198 

1  8 

42 

i69i 

1704 

1717 

i73o 

1742 

i755 

17 

42 

6210 

6222 

6234 

6247 

6259:6271 

17 

43 

1768 

1781 

1794 

1806 

1819 

i832 

16 

43 

6284 

6296 

63o8 

6320 

63336345 

16 

44 

i845 

i857 

1870 

i883 

1896 

1909 

i5 

44 

6357 

637o 

6382 

6394 

6406.6419 

i5 

45 

I92I 

i934 

1947 

1960 

1972 

I985 

i4 

45 

643  1 

6443 

6456 

6468 

648o 

6492 

i4 

46 

I998 

2OII 

2024 

2o36 

2049  2062 

i3 

46 

65o5 

65i7 

6529 

6542 

6554 

6566 

i3 

47 

2075 

2087 

2100 

2Il3 

2I262I38 

12 

47 

•  6578 

659i 

66o3 

66i5 

6627 

664o 

12 

48 

2l5l 

2  1  64 

2177 

2189 

2202 

22l5 

ii 

48 

665s 

6664 

6676 

6689 

6701 

67i3 

I  I 

49 

2228 

2240  2253 

2266 

2279 

2291 

10 

49 

6725 

6738 

675o 

6762 

6774 

6787 

IO 

5o 

9.9323o4 

2317 

2329 

2342 

2355 

2368 

9 

5o 

9.986799 

6811 

6823 

6836 

6848 

6860 

9 

5i 

52 

53 

238o 
2457 
2533 

2393 
2469 
2546 

2406 
2482 
2558 

2419  243i  2444 

2495|25o8  2520 

257i  2584  259-7 

8 
6 

5i 

52 

53 

6872  6884 
6946j6958 
7oi9  7o3i 

6897 
697o 

6909 
6982 
7o56 

6921  6933 
6994^007 
706817080 

8 
6 

54 

26o9 

2622 

2635 

2647 

26602673 

5 

54 

7o92 

7io4 

71  17  7129  7141  7i53 

5 

55 
56 

2685 
2762 

2698 
2774 

271  1 
2787 

2724  2736  2749 
2800  2812  2825 

4 
3 

55 
56 

7i65  7i78 
7238  725i 

7190  720217214  7226 
72637275  72877299 

4 
3 

57 

2838 

285o  2863 

2876 

2888  2901 

2 

57 

731273247336734873607372  2 

58 

2914 

2926 

2939 

2952 

2964  2977 

I 

58 

7385  7397  7409  7421  7433  7446  i 

59 

2990 

3002 

3oi5 

3028 

3o4o  3o53 

o 

59 

7458  7470:7482  7494  7506:75  1  S 

60" 

50" 

40"   30" 

20" 

10" 

a 

60"     50"   40"  i  30"   20"   10"   ^ 

Co-sine  of  3  1  Degrees. 

S 

Co-sine  of  30  Degrees.     s§  ! 

P  Part  S  !"   ~"   3"   4"   5"   6"  7" 

8"  9" 

o  T>  -*  U"  2"  3"  4"  5"  6"  7"  8"  3" 

"^13456 

8  9 

10  12      ut)  1   2   4   5   6   7   9  10  11 

LOGARITHMIC    TANGENTS. 


1 

Tangent  of  58  Degrees. 

c 

Tangent  of  59  Degrees. 

a 

0" 

10"   20" 

30" 

40" 

50" 

2 

0" 

10" 

20" 

30" 

40" 

50" 

O 

10.204211 

4258 

43o4 

435i 

4398 

4445 

5o 

0 

10.221226 

I274 

1322 

i369 

i4i7 

i465 

59 

i 

4492 

4539 

4586 

4633 

4679 

4726 

58 

I 

l5l2 

i56o 

1608 

i656 

I7o3 

i75i 

58 

2 

4773 

4820 

4867 

4914 

496i 

5oo8 

5? 

2 

I799 

1  846 

i894 

I942 

i99o 

2037 

57 

3 

5o54 

5ioi 

5i48 

5i95 

5242 

5289 

56 

3 

2o85 

2i332i8i 

2228 

2276 

2324 

56 

4 

5336 

5383 

543o 

5477 

5524 

557o 

55 

4 

2372 

94199467 

25i5 

2563 

26lO 

55 

5 

56i7 

5664 

57n 

5758 

58o5 

5852 

54 

5 

2658 

27o6 

2754 

2801 

2849 

2807 

54 

6 

5899 

5946 

5993 

6o4o 

6087 

6i34 

53 

6 

2945 

2993 

3o4o 

3o88 

3i36 

3i84 

53 

7 

6181 

6227 

6274 

632i 

6368 

64i5 

52 

7 

3232 

3279 

3327, 

3375 

3423 

347i 

52 

8 

6462 

65o9 

6556 

66o3 

665o 

6697 

5i 

8 

35i8 

3566 

36i? 

3662 

37io 

3757 

5i 

9 

6744 

6791 

6838 

6885 

6.932 

6979 

5o 

9 

38o5 

3853 

39oi 

3949 

3997 

4o44 

5o 

10 

10.207026 

7073 

7I20 

7i67 

72i4 

7261 

49 

10 

IO.224o92 

4i4o 

4i88 

4236 

4284 

4332 

49 

ii 

73o8 

7355 

7402 

7449 

7496 

7543 

48 

II 

4379 

4427 

4475 

4523 

457i 

46  1  9 

48 

12 

759o 

7637 

7684 

773i 

7778 

7825 

47 

12 

466? 

47i4 

4762 

48io 

4858 

49o6 

47 

i3 

7872 

7919 

7966 

8oi3 

8060 

8107 

46 

i3 

4954 

5002 

5o5o 

5o98 

5i45 

5i93 

46 

i4 

8i54 

8201 

8248 

8295 

8342 

8389 

45 

i4 

5241 

5289 

5337 

5385 

5433 

548  1 

45 

i5 

8437 

8484 

853! 

8578 

8625 

8672 

44 

i5 

5529 

5577 

5625 

5672 

5720 

5768 

44 

16 

87I9 

8766 

88i3 

8860 

80.07 

8954 

43 

16 

58i6 

5864 

59I2 

596o 

6008 

6o56 

43 

I7 

9001 

9048 

9o95 

9i43 

9i9o 

9237 

42 

17 

6io4 

6i52 

6200 

6248 

6296 

6344 

42 

18 

9284 

933i 

9378 

9425 

95i9 

4i 

18 

6392 

6440 

6488 

6535 

6583 

663i 

4i 

i9 

9566 

9614 

9661 

97o8 

9755 

98o2 

4o 

i9 

6679 

6727 

6775 

6823 

687i 

69i9 

4o 

20 

10.209849 

9896 

9943 

999  T 

..38 

..85 

39 

20 

io.226967 

7Oi5 

7o63 

7111 

7i59 

7207 

39 

21 

IO.2IOI32 

0179 

0226 

0273 

0321 

o368 

38 

21 

7255 

73o3 

735i 

7399 

7447 

7495 

38 

22 

o4i5 

0462 

0509 

o556 

o6o3 

o65i 

3y 

22 

7543 

759i 

7639 

7688 

7736 

7784 

37 

23 

0698 

o745 

0792 

o839 

0886 

o934 

36 

23 

7832 

7880 

7928 

7976 

8024 

8o72 

36 

24 

0981 

1028 

io75 

1122 

1170 

I2I7 

35 

24 

8120 

8168 

8216 

8264 

83i2 

836o 

35 

25 

1264 

i3n 

i358 

i4o5 

i453 

i5oo 

34 

25 

84o8 

8456 

85o4 

8552 

8601 

8649 

34 

26 

i547 

i594 

i64i 

i689 

1736 

i783 

33 

26 

8697 

8745 

8793 

884i 

8889 

8937 

33 

27 

i83o 

1878 

1925 

I972 

2OI9 

2066 

32 

27 

8985 

9o33 

9o8i 

9i3o 

9178 

9226 

32 

28 

2114 

2161 

2208 

2255 

23o3 

235o 

3i 

28 

9274 

9322 

937o 

94i8 

9466 

95i5 

3i 

29 

2397 

2444 

2492 

2539 

2586 

2633 

3o 

29 

9563 

96n 

9659 

97°7 

9755 

98o3 

3o 

So 

I0.2I268I 

2728 

2775 

2822 

2870 

29i7 

29 

3o 

I0.229852 

99oo 

9948 

9996 

..44 

.  .92 

29 

3i 

2964 

3OI2 

3io6 

3i53 

3201 

28 

3i 

io.23oi4o 

oi89 

0237 

0285 

o333 

o38i 

28 

32 

3248 

3295 

3343 

339o 

3437 

3484 

27 

32 

o429 

o478 

o52<5 

o574 

0622 

o67o 

27 

33 

3532 

3579 

3626 

3674 

3721 

3768 

26 

33 

o7i9 

0767 

o8i5 

o863 

o9n 

o96o 

26 

34 

38i6 

3863 

3910 

3958 

4oo5 

4o52 

25 

34 

1008 

io56 

no4 

Il52 

1201 

I249 

25 

35 

4ioo 

4i47 

4194 

4242 

4289 

4336 

24 

35 

I297 

1  345 

i394 

1442 

l49° 

i538 

24 

36 

4384 

443  1 

4478 

4526 

4573 

4620 

23 

36 

i586 

i635 

i683 

i73i 

1779 

1828 

23 

37 

4668 

47'5 

4762 

48io 

4857 

49o5 

22 

37 

i876 

I924 

i973 

2021 

2o69 

2II7 

22 

38 

4952 

4999 

5o47 

5o94 

5i4i 

5i89 

21 

38 

2166 

22l4 

2262 

23lO 

2359 

2407 

21 

39 

5236 

5284 

533i 

5378 

5426 

5473 

20 

39 

2455 

25o4 

2552 

26OO 

2648 

2697 

2O 

4o 

IO.2l552I 

5568 

56i5 

5663 

5710 

5758 

*9 

4o 

IO.232745 

2793 

2842 

2890 

2938 

2987 

19\ 

4i 

58o5 

5852 

5900 

5947 

5995 

6042 

18 

4i 

3o35 

3o83 

3i32 

3i8o 

3228 

3277 

18 

42 

6090 

6i37 

6i84 

6232 

6279 

6327 

17 

42 

3325 

3373 

3422 

347o 

35i8 

3567 

17 

43 

6374 

6422 

6469 

65i7 

6564 

6612 

16 

43 

36i5 

3663 

37I2 

376o 

38o8 

3857 

16 

44 

6659 

6706 

6754 

6801 

6849 

6896 

i5 

44 

39o5 

3953 

40O2 

4o5o 

4o99 

4i47 

i5 

45 

6944 

6991 

7o39 

7o86 

7i34 

•7181 

i4 

45 

4i95 

4244 

4292 

434o 

4389 

4437 

i4 

46 

7229 

7276 

7324 

737i 

7419 

7466 

i3 

46 

4486' 

4534 

4582 

463i 

4679 

4728 

i3 

47 

756i 

7609 

7656 

77o4 

775i 

12 

47 

4776 

4825 

4873 

492I 

497Q 

5oi8 

12 

48 

7799 

7846 

7894 

794i 

7989 

8o36 

II 

48 

5o67 

5n5 

5i64 

5212 

526o 

53o9 

II 

49 

8o84 

8i3i 

8i79 

8226 

8274 

8322 

10 

49 

5357 

54o6 

5454 

55o3 

555i 

56oo 

IO 

5o 

10.218369 

84i7 

8464 

85i2 

8559 

86o7 

9 

5o 

10,235648 

5696 

5745 

5793 

5842 

589o 

9 

5i 

8654 

8702 

875o 

8797 

8845 

8892 

8 

5i 

5939 

5987 

6o36 

6o84 

6i33 

6181 

8 

52 

8940 

8987 

9o35 

9083 

9i3o 

9i78 

7 

52 

623o 

6278 

6327 

6375 

6424 

6472 

7 

53 

9225 

9273 

9321 

9368 

94i6 

9463 

6 

53 

652i 

6569 

6618 

6666 

67i5 

6763 

6 

54 

95n 

9559 

9606 

9654 

97oi 

9749 

5 

54 

6812 

6860 

69o9 

6957 

7006 

7o55 

5 

55 

9797 

9844 

9892 

9939 

9987 

..35 

4 

55 

7io3 

7i52 

720O 

7249 

7297 

7346 

4 

56 

10.220082 

oi3o 

oi78 

0225 

0273 

0321 

3 

56 

7394 

7443 

7492 

754o 

7589 

7637 

3 

67 

o368 

o4i6 

o463 

o5n 

o559 

0606 

2 

5y 

7686 

7734 

7783 

7832 

7880 

7929 

2 

58 

o654 

0702 

o749 

°797 

o845 

o892 

I 

58 

7977 

802^ 

8o75 

8i23 

8172 

8220 

I 

59 

0940 

0988 

io36 

io83- 

n3i 

II79 

O 

59 

8*69 

83i8 

8366  84i5 

8463 

85i2 

O 

60" 

50" 

40" 

30" 

20" 

10" 

. 

60"     50"   40"   30"   20" 

10" 

d 

Co-tangent  of  31  Degrees. 

1 

Co-tangent  of  30  Degrees. 

3 

PPartJ1"  2"  3"  4//  5"  6"  7"  8//  9//  1  ppartJ1"  2"  3"  4//  5"  6"  7//  8//  9" 
a"^  5   9  14  19  24  28  33  38  43  |     irt{  5  10  14  19  24  29  34  39  43 

LOGARITHMIC    SINES. 


d 

Sine  of  60  Degrees. 

a 

Sine  of  61  Degrees. 

s 

0" 

10" 

20" 

30" 

40" 

50" 

Si 

0" 

10" 

20"  |  30" 

40" 

50" 

0 

9.937531 

7543 

7555 

7567 

7579 

759i 

59 

o 

9.941819 

i83i 

1843 

i854 

1866 

1878 

59 

I 

7604 

7616 

7628 

764o 

7652 

7664 

58 

I 

1889 

1901 

I9l3 

1924 

1936 

1948 

58 

2 

7676 

7689 

77oi 

77i3 

7725 

7737 

57 

2 

i959 

i97i 

i983 

i994 

2006 

2017 

57 

3 

7749 

776i 

7773 

7786 

7798 

7810 

56 

3 

2029 

2041 

2052 

2064 

20-76 

2087 

56 

4 

7822 

7834 

7846 

7858 

787o 

7883 

55 

4 

2099 

2III 

2122 

2i34 

2146 

2157 

55 

5 

7895 

7907 

79Z9 

793i 

7943 

7955 

54 

5 

2169 

2l8o 

2192 

22O4 

22l5 

2227 

54 

6 

7967 

7979 

7992  8oo4 

80168028 

53 

6 

2239 

2250 

2262 

2273 

2285 

2297 

53 

7 

8o4o 

8o52 

8o64  8o76 

80888100 

52 

7 

23o8 

2320 

233l 

2343 

2355 

2366 

52 

8 

8n3 

812$ 

81378149 

8161 

8i73 

5i 

8 

2378 

239o 

24OI 

24i3 

2424 

2436 

5i 

9 

8i85 

8197 

8209^221 

82338245 

5o 

9 

2448 

2459 

2471 

2482 

2494 

25o6 

5o 

10 

9.938258 

82-70 

8282^294 

83o683i8 

49 

10 

9.9425i7  2529 

254o 

2552 

2563 

2575 

49 

ii 

833o 

8342 

8354 

8366 

8378839o 

48 

1  1 

2587  25g8 

2610 

2621 

2633 

2645 

48 

12 

8402 

84i4 

84268439 

845i  8463 

47 

12 

26562668 

2679 

269I 

2-702 

27i4 

47 

i3 

8475 

8487 

8499 

85i  i 

85238535 

46 

i3 

2726 

2737 

2749 

2760 

2772 

2783 

46 

i4 

8547 

8559 

857i 

8583 

8595;86o7 

45 

i4 

2795 

2806 

2818 

283o 

284l 

2853 

45 

i5 

8619 

863i 

86438655 

8667!8679 

44 

i5 

2864 

2876 

2887 

2899 

2910 

2922 

44 

16 

8691 

87o3 

87i5 

8727 

8739875i 

43 

16 

2934 

2945 

2957 

2968 

2980 

2991 

43 

»7 

8763 

8776 

8788 

8800 

88128824 

42 

'7 

3oo3 

3oi4 

3026 

3o37 

3o4g 

3o6o 

42 

18 

8836 

8848 

8860  8872 

8884  8896 

4i 

18 

3o72 

3o83 

3o95 

3io7 

3n8 

3i3o 

4i 

20 

8908 
9.938980 

8920 
8992 

8932 
9004 

8944 
9oi6 

8956:8968 
902819040 

4o 
39 

20 

3i4i 
9.943210 

3i53 

3222 

3i64 
3233 

3i76 
3245 

3i87 
3256 

3i99 
3268 

4o 
39 

21 
22 

9123 

9064 
9i35 

9o769o8790999in 
9147  9159  9i7ifoi83 

38 
37 

21 
22 

3279 
3348 

329I 

336o 

3302 
337i 

33i4 
3383 

3325 
3394 

3337 
34o6 

38 
37 

23 

9i95 

9207 

9219  9231 

9243 

9255 

36 

23 

34i7 

3429 

344o 

3452 

3463 

3475 

36 

24 

9267 

9279 

9291 

93o3 

93i5 

9327 

35 

24 

3486 

3498 

35o9 

352i 

3532 

3543 

35 

25 

9339 

935i 

93639375 

93879399 

34 

25    3555 

3566 

3578 

3589 

36oi 

36i2 

34 

26 

94io 

9422 

94349446 

9458  94-70 

33 

26 

3624 

3635 

3647 

3658 

367o 

368i 

33 

27 

9482 

9494 

95069518 

95309542 

32 

27 

3693 

37o4 

37i5 

3727 

3738 

375o 

32 

28 

9554 

9566 

95789590 

9601  9613 

3i 

28 

376i 

3773 

3784 

3796 

38o7 

38i8 

3: 

29 

9625 

9637 

9649  9661 

9673  9685 

3o 

29 

383o 

384i 

3853 

3864 

3876 

3887 

3o 

3o 
3i 

9.939697 
9768 

9709 
9780 

9721  9733 

9792  9804 

97449756 

98169828 

29 

28 

3o 
3i 

9.943899 
3967 

39io 

3978 

3921 
3990 

4oov 

3944 
4oi3 

3956 
4024 

29 

28 

32 

9840 

9852 

9863  98-75 

9887  9899 

27 

32 

4o36 

4047 

4o58 

4070 

4o8i 

4o93 

27 

33 

9911 

9923 

9935  9947 

9959  997° 

26 

33 

4io4 

4u5 

4127 

4i38 

4i5o 

4i6i 

26 

34 

9982 

9994 

...6 

..18 

.  ,3o 

..42 

25 

34 

4172 

4i84 

4i95 

4207 

4218 

4229 

25 

359.940054 

oo65 

0077  0089  oioi 

oii3 

24 

35 

4241 

4252 

4264 

4275 

4286 

4298 

24 

36    oi25 

0/37 

oi48  0160  oi72 

oi84 

23 

36 

43o9 

432i 

4332 

4343 

4355 

4366 

23 

371    0196 

0208 

O22O  O23l 

0243 

0255 

22 

37 

4377 

4389 

44oo 

44i2 

4423 

4434 

22 

38    0267 

0279 

0291 

oTo°>  o3l4 

o326 

21 

38 

4446 

4457 

4468 

448o 

449i 

45o3 

21 

39    o338 

o35o 

o362 

o374o385 

o397 

2O 

39 

45i4 

4525 

4537 

4548 

4559 

457i 

2O 

4o9.94o4o9 

0421 

o433  o445  o456 

o468 

19 

4o 

9.944582 

4593 

46o5 

46i6 

4627 

4639 

I9 

4i 

o48o 

0492 

o5o4 

o5i6o5a7 

o539 

18 

4i 

465o 

466  1 

4673 

4684 

4696 

4707 

18 

42 

o55i 

o563 

o575 

o586  o598 

0610 

17 

42 

4718 

473o 

474i 

4752 

4764 

4775 

17 

43 

0622 

o634 

o645  o657  0669 

0681 

16 

43 

4786 

4798 

4809 

4820 

483i 

4843 

16 

44 
45 

0693 
o763 

o7o4 
o775 

o7i6  0728  0740 
0787^0799  081  1 

0752 
0822 

i5 
i4 

44 
45 

4854 
4922 

4865 
4933 

4877 
4945 

4888 
4g56 

4899 
4967 

4911 
4979 

i5 

i4 

46 

o834 

o846 

o858o87o 

0881 

o893 

i3 

46 

4990 

5ooi 

5oi3 

5o24 

5o35 

5o46 

i3 

47 

ogoS 

o9i7 

0928  0940 

0952 

0964 

12 

47 

5o58 

5069 

5o8o 

5092 

5io3 

5n4 

12 

48 

°975 

o987 

0999 

'  '  * 

IOII 

1023 

io34 

II 

48 

5i25 

5i37 

5i48 

5i59 

5171 

5i82 

II 

49 

io46 

io58 

10-70 

1081 

1093 

no5 

10 

49 

5i93 

52o4 

52i6 

522-7 

5238 

525o 

IO 

5o 

9.941117 

1128 

n4o 

Il52 

n64 

u75 

9 

5o 

9.945261 

5272 

5283 

5295 

53o6 

53i7 

9 

5i 

1187 

11  99 

I2II 

1222  1234 

1246 

8 

5i 

5328 

534o 

535i 

5362 

5374 

5385 

8 

52 

1258 

1269 

I28l 

i293  i3o4 

i3i6 

7 

52 

5396 

54o7 

54i9 

543o 

544i 

5452 

7 

53 

i328 

1  34o 

i35i 

i363  i375 

1387 

6 

53 

5464 

5475 

5486 

5497 

55o9 

5520 

6 

54    i398 

i4io 

1422 

i433  i445 

1457 

5 

54 

553i 

55425554 

5565 

5576 

5587 

5* 

55    i469 
56    i539 

i48o 
i55o 

1492 
i562 

i5o4 

i574 

i5i5 
1  586 

1527 
i597 

4 
3 

55 
56 

5598 
5666 

56io562i 

5677!5688 

5632 
5700 

5643 

5-7II 

5655 
5722 

4 
3 

57 

1609 

1621 

i632 

1  644  1  656 

1667 

2 

57 

5733  5744|5756 

57675778 

5789 

2 

58    i679 

1691 

I702 

I7l4  1726 

1738 

I 

58 

58oo  58125823  5834  5845 

5857 

I 

59j    *749 

1761 

i773 

i784!i796 

1808 

O 

59 

5868:5879  589o59oi!59i3 

5924 

O 

60"     50"  |  40" 

30"   20"   10" 

d 

60"     50"   40"  |  30"   20" 

10" 

d 

Co-sine  of  29 

Degrees. 

§ 

Co-sine  of  28  Degrees. 

5 

P  TartJ  J"  2"  3"  4" 

5"  6"  7"  8"  9" 

^  1"  2"  V  4"  5"  6"  7"  8"  9" 

6   7   8  10  11 

irtfc  1   2   3   5   6   7   8   9  10 

LOGARITHMIC    TANGENTS. 


•I 

Tangent  of  60  Degrees. 

d 

£« 

Tangent  of  61  Degrees. 

s 

0" 

10" 

20" 

30" 

40"  \  50" 

2 

0" 

10" 

20" 

30" 

40" 

50" 

o 

10.  23856i 

8609 

8658 

8707 

8755 

88o4 

59 

0 

10.256248 

6298 

6347 

6397 

6447 

6496 

59 

i 

8852 

8901 

8g5o 

8998 

9047 

9096 

58 

I 

6546 

6596 

6645 

6695 

6745 

6794 

58 

2 

9144 

9193 

9242 

9290 

9339 

9388 

57 

2 

6844 

6894 

6944 

6993 

7o43 

7o93 

57 

3 

9436 

9485 

9534 

9582 

963i 

9680 

56 

3 

7142 

7192 

7242 

7291 

734i 

739i 

56 

4 

9728 

9777 

9826 

9874 

9923 

9972 

55 

4 

744i 

7490 

754o 

759° 

764o 

7680 

55 

5 

10.240021 

0069 

0118 

0167 

02l5 

0264 

54 

5 

7739 

7789 

7839 

7888 

7938 

7988 

54 

6 

o3i3 

o362 

o4io 

0459 

o5o8 

o557 

53 

6 

8o38 

8087 

8i37 

8187 

82378286 

53 

7 

o6o5 

o654 

0703 

0752 

0800 

0849 

52 

7 

8336 

8386 

8436 

8486 

85358585 

52 

8 

0898 

0947 

o995 

io44 

1093 

1142 

5i 

8 

8635 

8685 

8735 

8784 

8834 

8884 

5i 

9 

1190 

1239 

1288 

i337 

i385 

1434 

5o 

9 

8934 

8984 

9o33 

9o83 

9i33 

9i83 

5o 

10 

io.24i483 

i532 

1681 

1629 

1678 

1727 

49 

10 

io.259233 

9283 

9332 

9382 

9432 

9482 

49 

ii 

1776 

i825 

i873 

1922 

1971 

2O2O 

48 

1  1 

9532 

9582 

9632 

968i 

973i 

9781 

48 

12 

2069 

2118 

2166 

22l5 

2264 

23l3 

47 

12 

983i 

988i 

993i 

998i 

..3i 

..80 

47 

i3 

2362 

24n 

2459 

25o8 

2557 

2606 

46 

i3 

io.26oi3o 

0180 

023O 

0280 

o33o 

o38o 

46 

i4 

2655 

2704 

2753 

2801 

285o 

2899 

45 

i4 

o43o 

o48o 

o53o 

o58o 

o629 

0679 

45 

i5 

2948 

2997 

3o46 

3o95 

3i43 

3l92 

44 

i5 

0729 

0779 

0829 

o879 

0929 

°979 

44 

16 

324l 

3290 

3339 

3388 

3437 

3486 

43 

16 

1029 

1079 

1129 

"79 

1229 

i279 

43 

17 

3535 

3584 

3632 

368i 

373o 

3779 

42 

17 

1329 

i379 

1429 

i479 

1529 

i579 

42 

18 

8828 

3877 

3926 

3975 

4024 

4o73 

4i 

18 

1629 

1679 

I729 

i779 

1829 

1879 

4i 

19 

4l22 

4i7i 

4220 

4269 

43i8 

4366 

4o 

J9 

1929 

1979 

2029 

2079 

2129 

2179 

4o 

20 

i  O.2444  i  5 

4464 

45i3 

4562 

46n 

466o 

39 

20 

10.262229 

2279 

2329 

2379 

2429 

2479 

39 

21 

4709 

4758 

48o7 

4856 

4905 

4954 

38 

21 

2529 

2579 

2629 

2679 

2729 

2779 

38 

22 

5oo3 

5o52 

5ioi 

5i5o 

5i99 

5248 

37 

22 

2829 

2879 

2929 

2979 

3029 

3°79 

37 

23 

5297 

5346 

5395 

5444 

5493 

5542 

36 

23 

3i3o 

3i8o 

3230 

328o 

333o 

338o 

36 

24 

559i 

564o 

5689 

5738 

5787 

5836 

35 

24 

343o 

348o 

353o 

358o 

363o 

368  1 

35 

25 

5885 

5934 

5984 

6o33 

6082 

6i3i 

34 

25 

373i 

378i 

383i 

388i 

393i 

398i 

34 

26 

6180 

6229 

6278 

632  7 

6376 

6425 

33 

26 

4o3i 

4082 

4l32 

4182 

4232 

4282 

33 

27 

6474 

6523 

65?2 

6621 

6670 

672O 

32 

27 

4332 

4382 

4433 

4483 

4533 

4583 

32 

28 

6769 

6818 

6867 

69i6 

6965 

7oi4 

3i 

28 

4633 

4683 

4734 

4784 

4834 

4884 

3i 

29 

7063 

7112 

7161 

7211 

7260 

73o9 

3o 

29 

4934 

4985 

5o35 

5o85 

5i35 

5i85 

3o 

3o 

10.247358 

7407 

7456 

75o5 

7554 

7604 

29 

3o 

10.265236 

5286 

5336 

5386 

5436 

5487 

29 

3r 

7653 

7702 

775! 

7800 

7849 

7899 

28 

3i 

5537 

5587 

5637 

5688 

5738 

5788 

28 

32 

7948 

7997 

8o46 

8o95 

8i44 

8i94 

27 

32 

5838 

5889 

5939 

5989 

6039 

6o9o 

27 

33 

8243 

8292 

834i 

839o 

8439 

8489 

26 

33 

6i4o 

6190 

6240 

6291 

634i 

639i 

26 

34 

8538 

8587 

8636 

8685 

8735 

8784 

25 

34 

6442 

6492 

6542 

6592 

6643 

6693 

25 

35 

8833 

8882 

893i 

898i 

9o3o 

9°79 

24 

35 

6743 

6794 

6844 

6894 

6945  6995 

24 

36 
3? 

9128 
9424 

9178 
9473 

9227 
9522 

9276 

9572 

9325 

962I 

9375 
967o 

23 
22 

36 
37 

7o45 
7347 

7096 
7398 

7i46 

7448 

7196 

7498 

72477297 
75497^99 

23 
22 

38 

9719 

9769 

98i8 

9867 

99i6 

9966 

21 

38 

?649 

7700 

775o 

7800 

785  1  7901 

21 

39 

io.25ooi5 

oo64 

on4 

oi63 

0212 

0261 

20 

39 

7952 

8002 

8o52 

8io3 

8i5382o4 

2O 

4o 

io.25o3n 

o36o 

0409 

0459 

o5o8 

o557 

J9 

4o 

10.268254 

83o4 

8355 

84o5 

8456  85o6 

'9 

4i 

0607 

o656 

0705 

o755 

o8o4 

o853 

18 

4i 

8556 

8607 

8657 

8708 

8758 

8809 

18 

42 

0903 

O952 

IOOI 

io5i 

IIOO 

1149 

*7 

42 

8859 

8909 

896o 

9010 

9061 

9111 

«7 

43 

1199 

1248 

1297 

1  347 

i396 

i445 

16 

43 

9162 

9212 

9263 

93i3 

936494i4 

16 

44 

i495 

1  544 

i594 

1  643 

1692 

1742 

i5 

44 

9465 

95i5 

9566 

9616 

966797i7 

i5 

45 

1791 

i84o 

1890 

i939 

1989 

2o38 

x4 

45 

9767 

98i8 

9868 

9919 

9970  .  .20 

i4 

46 

2087 

2137 

2186 

2236 

2285 

2335 

i3 

46 

10.270071 

0121 

0172 

O222 

0273  o323 

i3 

47 

2384 

2433 

2483 

2532 

2582 

263i 

12 

47 

o374 

O424 

o475 

0525 

0576  0626 

12 

48 

2681 

2730 

2779 

2829 

2878 

2928 

II 

48 

0677 

0728 

0778 

0829 

o879  0930 

II 

49 

2977 

3027 

3o76 

3i26 

3i75 

3225 

10 

49 

0980 

io3i 

1082 

Il32 

u83  1233 

IO 

5o 

10.253274 

3324 

3373 

3423 

3472 

352i 

9 

5o 

10.271284 

i335 

i385 

i436 

i486  i537 

9 

5i 

357i 

3620 

3670 

37i9 

3769 

38i8 

8 

5i 

i588 

i638 

i689 

i739 

1790  i84i 

8 

52 

3868 

39i8 

3967 

4017 

4o66 

4n6 

7 

52 

1891 

1942 

i993 

2o43 

2094  2i45 

7 

53 

4i65 

42i5 

4264 

43i4 

4363 

44i3 

6 

53 

2195 

2246 

2297 

2347 

23982449 

6 

54 

4462 

45i2 

456i 

46n 

466i 

4710 

5 

54 

2499 

255o 

26OI 

265i 

2702  2733 

5 

55 

4760 

48o9 

4859 

4908 

4958 

5oo8 

4 

55 

28o3 

2854 

29o5 

2955 

3oo63o57 

4 

56 

5o57 

5107 

5i56 

5206 

5256 

53o5 

3 

56 

3io8 

3i58 

3209 

3260 

33io336i 

3 

57 

5355 

54o4 

5454 

55o4 

5553 

56o3 

2 

57 

3412 

3463 

35i3 

3564 

36i53666 

2 

58 

5652 

5702 

5752 

58oi 

585i 

5901 

I 

58 

37i6 

3767 

38i8 

3869 

391913970 

I 

59 

595o 

6000 

6049 

6099 

6:49 

6198 

0 

59 

4O2I 

4072 

4l22 

4i73 

4224*4275 

O 

60" 

50" 

40" 

30"  \  20"   10" 

d 

60"      50" 

40" 

30" 

20"  j  10" 

d 

Co-tangent  of  29  Degrees. 

•H 

s 

Co-tangent  of  28  Degrees. 

•fl 

S 

p  pa  *5  r/  2"  3//  4"  -5"  6"  7//  8"  9" 

.(  1"  2"  3"  4"  5"  6"  7"  8"  9" 

irl\  5  10  15  20  25  29  34  39  44 

Lrt)  5  10  15  20  25  30  35  40  45 

LOGARITHMIC    SINES. 


N 

Sine  of  62  Degrees. 

J 

Sine  of  63  Degrees. 

1  * 

0"     10"  '  20" 

30"   40"   50" 

2 

0" 

10" 

20" 

30" 

40" 

50" 

0 

9.945935  5g46  5967  5969  5980 

599i  59 

O 

9.94988i 

9892 

99O2 

99i3 

9924 

9935 

59 

I 

6002 

6oi36o246o366o47 

6o58 

58 

I 

9945 

9956 

9967 

9977 

9988 

9999 

58 

2 

6069 

6080  6o92  6zo36n4 

6i25 

57 

2 

9.950010 

O02O 

oo3i 

0042 

OO52 

oo63 

57 

3 

6i36 

6i476i596i7o6i8i 

6i92 

56 

\ 

0074 

0084 

oo95 

0106 

0117 

0127 

56 

4 

6203 

62146226623-76248 

6259 

55 

I 

oi38 

oi49 

oi59 

0170 

0181 

oioi 

55 

5 

6270 

6281  6293 

63o463i5 

632654 

f 

O202 

02  I  ^ 

022^ 

0234 

0245 

0256 

54 

6 

6337 

6348  635$ 

637ii6382 

639353 

6 

0266 

0277 

0288 

0298 

o3o9 

0320 

53 

7 

64o4 

64i56426 

6437'6449 

646o  52 

7 

o33o 

o34i 

o352 

o362 

o373 

o384 

52 

8 

6471 

6482649365o465i5 

6526  5i 

8 

o394 

o4o5 

o4i6 

0426 

o437 

o448 

5i 

9 

6538  6549  656o657i:6582 

6593 

5o 

9 

o458 

o469 

o48o 

o49o 

o5oi 

O5l2 

5o 

10 

9.94660^ 

66i5662766386649 

6660 

49 

10 

9.95o522 

o533 

o544 

o554 

o565 

0576 

49 

ii 

6671 

6682  6693  6704:6715 

6726 

48 

ii 

o586 

o597 

0607 

0618 

o629 

o639 

48 

12 

6738 

6749  676o  6771  6782 

6793 

47 

12 

o65o 

0661 

0671 

0682 

o693 

0703 

47 

i3 

68o4 

68i5682668376849 

6860 

46 

i3 

071^ 

0724 

o735 

o746 

o756 

0767 

46 

i4 

6871 

6882  689369046915 

6926 

45 

i4 

0778 

0788 

°799 

o8o9 

0820 

o83i 

45 

i5 

6937 

6948  6959  697o|6982 

6993 

44 

i5 

o84i 

o852 

0862 

o873 

o884 

o894 

44 

16 

700^ 

7oi5  7026.7037 

7048 

7o59 

43 

16 

o9o5 

o9i5 

0926 

o937 

o947 

o958 

43 

ll 

7070 

7o8i  7o92 

7io3 

7ii4 

7i25 

42 

17 

o968 

°979 

o99o 

IOOO 

IOII 

1021 

42 

18 

7i36 

7i477i58 

7i7o 

7181 

7I92 

4i 

18 

1032 

io43 

io53 

io64 

1074 

1  08  5 

4i 

'9 

720: 

72l4  7225 

7236 

7247 

7258 

4o 

i9 

io96 

1106 

1117 

1127 

n38 

n48 

4o 

20 

9.947269 

7280  729I 

7302 

73i3 

7324 

39 

20 

9.95n59 

1170 

1180 

n9i 

I2OI 

1212 

39 

21 

7335 

73467357 

7368 

7379 

739o 

38 

21 

1222 

1233 

1244 

1254 

1265 

I275 

38 

22 

74oi 

74i2  7423 

,7434 

7445 

7456 

37 

22 

1286 

I296 

i3o7 

i3i7 

i328 

i339 

37 

23 

7467 

7478  7489  75oo 

7611 

7522 

36 

23 

i349 

i36o 

1370 

i38i 

i39i 

1402 

36 

24 

7533 

754575567567 

7578 

7589 

35 

24 

l4l2 

i423 

i434 

1  444 

i455 

i465 

35 

25 

•7600 

76n  -7622 

7633 

7644 

7655 

34 

25 

1476 

i486 

i497 

i5o7 

i5i8 

i528 

34 

26 

7665 

7676  7687  7698  77o9 

7720 

33 

26 

i539 

i549 

i56o 

i57o 

i58i 

i59i 

33 

27 

773i 

7742  7753 

7764I7775 

7786 

32 

27 

1602 

i6i3 

1623 

i634 

1  644 

i655 

32 

28 

7797 

78o878i9 

783o 

7^41 

7852 

3i 

28 

i665 

1676 

1686 

i697 

1707 

1718 

3i 

29 

7863 

7874  7885 

7896 

79°7 

79i8 

3o 

29 

1728 

i739 

i749 

1760 

1770 

1781 

3o 

3o 

9-947929 

794o  795i  7962 

7973 

7084 

29 

3o 

9.95i79i 

1802 

1812 

1823 

i833 

1  844 

29 

3i 

7995 

8006801-78028 

8o38  8o49 

28 

3i 

i854 

i865 

i875 

1886 

i896 

1007 

28 

32 

8060 

8o7i  8082  8o93 

8io48n5 

27 

32 

I9i7 

I928 

i938 

i949 

i959 

i969 

27 

33 

8126 

8i378i48,8i59 

8x708181 

26 

33 

I98o 

i99o 

2001 

201  I 

2022 

2032 

26 

34 

8l92 

8203  82138224 

82358246 

25 

34 

2o43 

2o53 

2064 

2074 

2085 

2O05 

25 

35 

8257 

8268  8279 

8290 

83oi  83i2 

24 

35 

2106 

2116 

2126 

2137 

2147 

2i58 

24 

36 

8323 

8334  8344 

8355 

8366  8377 

23 

36 

2168 

2179 

2l89 

22OO 

2210 

2221 

23 

3? 

8388 

839984io 

8421 

8432  8443 

22 

37 

223l 

2252 

2262 

2273 

2283 

22 

38 

8454 

8464  8475 

8486 

8497  85o8 

21 

38 

2294 

23o4 

23l4 

2325 

2335 

2346 

21 

39 

85i9 

853o854i 

8552 

8562  8573 

2O 

39 

2356 

2367 

2377 

2387 

2398 

2408 

20 

4o 

9.948584 

8595  8606 

8617 

8628 

863o 

I9 

4o 

9.9524i9 

2429 

2440 

2460 

2471 

!9 

4i 

865o 

8660  867i 

8682 

8693  8704 

18 

4i 

2481 

2492 

25O2 

2512 

2523 

2533 

18 

42 

87i5 

87268736 

8747 

87588769 

'7 

42 

2544 

2554 

2565 

2575 

2585 

2596 

17 

43 

878o 

879i  8802 

8812 

8823  8834 

16 

43 

2606 

2617 

2627 

2637 

2648 

2658 

6 

44 

8845 

8856  8867 

8878 

8888  8899 

i5 

44 

2669 

2679 

2689 

2700 

2710 

2720 

5 

45 

89io 

892i  8932 

8943 

895t4;8964 

i4 

45 

2731 

2741 

2752 

2762 

2772 

2783 

4 

46 

8975 

89868997 

9008 

9019^029 

i3 

46 

2793 

28o3 

2814 

2824 

2835 

2845 

3 

47 

9o4o 

9o5i  9062 

9o73 

9083  9094 

12 

47 

2855 

2866 

2876 

2886 

2807 

2907 

2 

48 

9io5 

9116  912-7 

9i38 

91489169 

II 

48 

29l8 

2928 

2938 

2949 

2959 

2969 

I 

49 

9i7o 

918119192 

9202 

9213  9224 

IO 

49 

298o 

2990 

3ooo 

3on 

3021 

3o3i 

O 

5o 

5i 

9.949235 
93oo 

92469256 
93109321 

9267 
9332 

92-789289 
9343  9354 

I 

5o 
5i 

3io4 

3o52 
3n4 

3o62 
3i24 

3o73 
3i35 

3o83 
3i45 

3o93 
3i55 

I 

52 

.  9364 

9375[9386 

9397 

94089418 

1 

52 

3i66 

3176 

3i86 

3i97 

3207 

3217 

7 

53 

9429 

944o'945i 

9462 

9472  9483 

6 

53 

3228 

3238 

3248  3259 

3269 

3279 

6 

54 

9494 

95o595i5 

9526 

9537  9548 

5 

54 

329o 

33oo 

331013321 

333i 

334i 

5 

55 
56 

9558 
0623 

96699680 

96349645 

9591 
9655 

9602  9612 
9666  9677 

4 
3 

55 
56 

33523362337213382 

3413342434343444 

3393  34o3 
3455  3465 

4 
3 

57 

9688  9698  9709  9720 

973i  974i 

2 

57 

3475  3485  3496  35o6;35i6  3527 

2 

58 

9752J976397749784 

9795  98o6 

I 

58 

3537  3547'3557  3568  3578  3588  i 

59 

9816(982719838  9849  9859  987o 

O 

59 

359936o936i9  3629  364o365o  o 

60"     50"  i  40" 

30"   20"   10" 

. 

60"     50"   40"   30"   30"   10" 

Co-sine  of  27 

Degrees.     a 

Co-sine  of  26  Degrees. 

(  1  //   O"   Q"   AH 

P  Part)        **   4 
fft{  1   2   3   4 

5   7   8   9  10   P-Part|  i  ~2   3456789 

LOGARITHMIC    TANGENTS. 


87 


1 

Tangent  of  62  Degrees. 

.5 

Tangent  of  63  Degrees. 

91 

0" 

10" 

2O' 

30" 

40" 

50" 

8 

0" 

10" 

20" 

30" 

40" 

50" 

o 

10.274326 

4376 

4427 

4478 

4529 

458o 

59 

0 

10.292834 

2886 

2938 

299O 

3o42 

3o94 

59 

i 

463o 

468i 

4?32 

4783 

4834 

4885 

58 

i 

3i46 

3i99 

325i 

33o3 

3355 

34o7 

58 

2 

4935 

4986 

5o37 

5o88 

5i39 

5i9o 

57 

2 

3459 

35n 

3563 

36i5 

3667 

372O 

57 

3 

524o 

5291 

5342 

5393 

5444 

5495 

56 

3 

3772 

3824 

3876 

3928 

398o 

4o32 

56 

4 

5546 

5597 

5647 

5698 

5749 

58oo 

55 

4 

4o84 

4i37 

4i89 

4241 

4293 

4345 

55 

5 

585i 

5902 

5953 

6oo4 

6o55 

6io5 

54 

5 

4397 

4449 

45o2 

4554 

46o6 

4658 

54 

6 

6i56 

6207 

6258 

63o9 

636o 

64n 

53 

6 

4710 

4763 

48i5 

4867 

49i9 

497i 

53 

7 

6462 

65i3 

6564 

66i5 

6666 

67i7 

52 

7 

5o24 

5076 

5i28 

5i8o 

5232 

5285 

52 

8 

6768 

6819 

6870 

6920 

697i 

7022 

5i 

8 

5337 

5389 

544  1 

5494 

5546 

5598 

5i 

9 

7o73 

7124 

7i75 

7226 

7277 

7328 

5o 

9 

565o 

5703 

5755 

58o7 

5859 

59I2 

5o 

10 

io.277379 

743o 

748  1 

7532 

7583 

7634 

49 

10 

io.295964 

6016 

6068 

6121 

6i73 

6225 

49 

ii 

7685 

7736 

7787 

7838 

7889 

7940 

48 

ii 

6278 

633o 

6382 

6434 

6487 

6539 

48 

12 

7991 

8o43 

8o94 

8i45 

8i96 

824-7 

47 

12 

659i 

6644 

6696 

6748 

6801 

6853 

47 

i3 

8298  8349 

84oo 

845  1 

85o2 

855^3 

46 

i3 

69o5 

6958 

7010 

7062 

7n5 

7i67 

46 

i4 

86o4 

8655 

8706 

8757 

88o9 

8860 

45 

i4 

72I9 

7272 

?324 

7377 

7429 

748  1 

45 

i5 

8911 

8962 

9oi3 

9o64 

9n5 

9i66 

44 

i5 

7534 

7586 

7638 

7691 

7743 

7796 

44 

16 

9217 

9268 

9320 

937i 

9422 

9473 

43 

16 

7848 

79oo 

7953 

8oo5 

8o58 

8110 

43 

i? 

9524 

9575 

9626 

9678 

9729 

978o 

42 

J7 

8i63 

82i5 

826? 

8320 

8372 

8425 

42 

18 

983i 

9882 

9933 

9984 

..36 

..87 

4i 

18 

8477 

853o 

8582 

8635 

8687 

874o 

4i 

J9 

10.  280138 

0189 

O24o 

0292 

o343 

o394 

4o 

:9 

8792 

8845 

8897 

8949 

9002 

9o54 

4o 

20 

io.28o445 

0496 

o548 

o599 

o65o 

0701 

39 

20 

IO.299IO7 

9i59 

92I2 

9264 

93i7 

937o 

39 

21 

0752 

0804 

o855 

o9o6 

o957 

ioo9 

38 

21 

9422 

9475 

9527 

958o 

9632 

9685 

38 

22 

1060 

mi 

1162 

I2l4 

1265 

i3i6 

37 

22 

9737 

979° 

9842 

9895 

9947 

.... 

37 

23 

i367 

1419 

1470 

l52I 

l572 

1624 

36 

23 

io.3ooo53 

oio5 

oi58 

0210 

O263 

o3i5 

36 

24 

i675 

I726 

1777 

l829 

1880 

i93i 

35 

24 

o368 

0421 

o473 

o526 

o578 

o63i 

35 

25 

1983 

2o34 

2o85 

2l37 

2188 

2239 

34 

25 

o684 

0736 

o789 

o84i 

o894 

o947 

34 

26 

2291 

2342 

2393 

2445 

2496 

2547 

33 

26 

°999 

IO52 

no5 

1167 

I2IO 

1263 

33 

27 

2599 

265o 

2701 

2753 

2804 

2855 

32 

27 

i3i5 

1  368 

1421 

i473 

i526 

i579 

32 

28 

2907 

2958 

3oo9 

3o6i 

3lI2 

3i64 

3i 

28 

i63i 

1  684 

i737 

1789 

1842 

i895 

3i 

29 

32i5 

3266 

33i8 

3369 

3421 

3472 

3o 

29 

i947 

2OOO 

2o53 

2106 

2i58 

2211 

3o 

3o 

ic.  283523 

3575 

3626 

3678 

3729 

378o 

29 

3o 

IO.  3O2264 

23i6 

2369 

2422 

2475 

2527 

29 

3i 

3832 

3883 

3935 

3986 

4o38 

4o89 

28 

3i 

258o 

2633 

2686 

2738 

279I 

2844 

28 

32 

4i4o 

4192 

4243 

4295 

4346 

4398 

27 

32 

2897 

295o 

3OO2 

3o55 

3io8 

3i6i 

27 

33 

4449 

45oi 

4552 

46o4 

4655 

4707 

26 

33 

32i3 

3266 

33i9 

3372 

3425 

3478 

26 

34 

4?58 

48io 

486i 

49i3 

4964 

5oi6 

25 

34 

353o 

3583 

3636 

3689 

3742 

3794 

25 

35 

5o67 

5ii9 

5170 

5222 

5273 

5325 

24 

35 

3847 

39oo 

3953 

4oo6 

4o59 

4112 

24 

36 

5376 

5428 

5479 

553i 

5582 

5634 

23 

36 

4i64 

4217 

4270 

4323 

4376 

4429 

23 

37 

5686 

5737 

5789 

584o 

5892 

5943 

22 

37 

4482 

4535 

4588 

464o 

4693 

4746 

22 

38 

5995 

6046 

6o98 

6i5o 

6201 

6253 

21 

38 

4799 

4852 

49o5 

4958 

Son 

5o64 

21 

39 

63o4 

6356 

64o8 

6459 

65n 

6562 

2O 

39 

5n7 

5170 

5223 

5276 

5328 

538i 

20 

4o 

10.286614 

6666 

6717 

6y69 

6821 

6872 

I9 

4o 

io.3o5434 

5487 

554o 

5593 

5646 

5699 

J9 

4i 

6924 

6975 

7027 

7°79 

7i3o 

7182 

18 

4i 

5752 

58o5 

5858 

Sgii 

5964 

6oi7 

18 

42 

7234 

?285 

7337 

7389 

744o 

7492 

17 

42 

6o7o 

6i23 

6i76 

6229 

6282 

6335 

!7 

43 

7544 

7595 

7647 

7699 

775i 

7802 

16 

43 

6388 

644i 

6494 

654? 

6600 

6654 

16 

44 

7854 

79o6 

7957 

8oo9 

8061 

8n3 

i5 

44 

67o7 

6760 

68i3 

6866 

69i9 

6972 

i5 

45 

8i64 

8216 

8268 

83i9 

837i 

8423 

i4 

45 

7O25 

7078 

7i3i 

7i84 

7237 

729o 

i4 

46 

8475 

8526 

8578 

863o 

8682 

8733 

i3 

46 

7344 

7397 

745o 

75o3 

7556 

76o9 

i3 

47 

8785 

8837 

8889 

894i 

8992 

9o44 

12 

47 

7662 

77i5 

7768 

7822 

7875 

7928 

12 

48 

9o96 

9i48 

9i99 

925l 

93o3 

9355 

II 

48 

798i 

8o34 

8o87 

8i4i 

8i94 

8247 

II 

49 

9407 

9458 

95io 

9562 

96-14 

9666 

IO 

49 

83oo 

8353 

84o6 

846o 

85i3 

8566 

IO 

5o 

10.289718 

9769 

982I 

9873 

9925 

9977 

9 

5o 

io.3o86i9 

8672 

8726 

8779 

8832 

8885 

9 

5i 

10.290029 

0081 

Ol32 

0184 

0236 

0288 

8 

5i 

8938 

8992 

9o45 

9098 

9i5i 

92o5 

8 

52 

o34o 

o392 

o444 

0496 

o547 

o599 

7 

52 

9258 

93n 

9364 

94i8 

947i 

9524 

7 

53 

o65i 

0703 

o755 

0807 

o859 

0911 

6 

53 

9577 

963i 

9684 

9737 

979° 

9844 

6 

54 

0963 

ioi5 

1066 

1118 

II70 

1222 

5 

54 

9897 

995o 

...4 

..57 

.  no 

.164 

5 

55 

1274 

i326 

1378 

i43o 

1482 

i534 

4 

55 

10.810217 

0270 

0324 

o377 

o43o 

o484 

4 

56 

i586 

i638 

i69o 

1742 

i794 

1  846 

3 

56 

o537 

oSgo 

o644 

o697 

o75o 

0804 

3 

57 

1898 

I95o 

2OO2 

2054 

2106 

2i58 

2 

57 

o857 

0910 

o964 

ioi7 

IO7O 

1124 

2 

58 

2210 

2262 

23i4 

2366 

2418 

2470 

I 

58 

1177 

I23l 

1284 

I337 

i39i 

1  444 

I 

59 

2522 

2574 

2626 

2678 

273o 

2782 

0 

59 

i498 

i55i 

i6o5 

i658 

i7ii 

i765 

O 

60" 

50" 

40" 

30" 

20" 

10" 

f« 

60"      50"   40"  |  30" 

20" 

10" 

. 

Co-tangent  of  27  Degrees. 

S 

Co-tangent  of  26  Degrees. 

i 

P  Part  5  l"   2"   3"   4//   5//   6//   7"   8"   9" 

.<  1"  2"  3"  4"  -5"  6"  7"  8"  9" 

}  5  10  15  21  26  31  36  41  46 

lrt{  5  11  16  21  26  32  37  42  47 

88 


LOGARITHMIC    SINES. 


t 

Sine  of  64  Degrees.     , 

d 

Sine  of  65  Degrees. 

s 

0" 

10" 

20" 

30" 

40" 

50" 

9 

0"    i  10"  |  20"  [  30"   40" 

50" 

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58 

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2 

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20 

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20 

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21 
22 

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38 
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21 
22 

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8522 

858o 

8532 
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8542 
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38 
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23 

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36 

23 

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9080 

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22 

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21 

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39 
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9.960052 

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0674:0683  069^  0702  071  1  071: 

60" 

50" 

40" 

30"  |  20" 

10" 

d 

60"    |  50"   40"  j  30"   20"  j  10"  i  ^ 

Co-sine  of  25 

Degrees. 

Co-sine  of  24  Degrees.     a 

T  PartJ  l"  2"  3"  4" 
I.lartJ  !   2  3  4 

5"  6"  7"  8"  9" 
56789 

.(  1"  2"  3"  4"  5"  6"  7"  fi 
irt\  1   2   3   4   5   6   7   *   !> 

LOGARITHMIC    TANGENTS. 


c 

Tangent  of  64  Degrees. 

Jj 

Tangent  of  65  Degrees. 

9 

0" 

10"  1  20" 

30" 

40" 

50" 

s 

0" 

10" 

20" 

30" 

40" 

50" 

0 

io.3n8i8 

l872JI925 

i979 

2032 

2o85 

59 

0 

io.33i327 

i382 

i437 

1492 

1  547 

1602 

59 

i 

2l39 

2I92  2246 

2299 

2353 

2406 

58 

I 

i657 

I7I2 

i767 

1822 

i877 

1932 

58 

2 

2460 

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2620 

2674 

2727 

5? 

2 

i987 

2042 

2097 

2i53 

2208 

2263 

57 

3     2781 

2834 

2888 

294l 

2995 

3o48 

56 

3 

23i8 

2373 

2428 

2483 

2538 

2593 

56 

A     3io2 

3i55 

3209 

3263 

33i6 

337o 

55 

4 

2648 

2703 

2758 

28i3 

2868 

2924 

55 

5,     3423 

3477 

353o 

3584 

3637 

369i 

54 

5 

2979 

3o34 

3089 

3i44 

3i99 

3254 

54 

6 

3745 

3798 

3852 

39o5 

3959 

4oi3 

53 

6 

33o9 

3364 

3420 

3475 

353o 

3585 

53 

7 

4o66 

4l2O 

4i73 

4227 

4281 

4334 

52 

7 

364o 

3695 

375i 

38o6 

386i 

39i6 

52 

8 

4388 

4442 

4495 

4549 

46o3 

4656 

5i 

8 

397i 

4026 

4082 

4i37 

1" 

|ij.  —  .4  j 

5i 

9 

4710 

4764 

48i7 

487i 

4925 

4978 

5o 

9 

43o2 

4358 

44i3 

4468 

H  — 

4579 

5o 

10 

io.3i5o32 

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5i39 

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5247 

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49 

io.334634 

4689 

4744 

48oo 

4855 

4910 

49 

ii 

5354 

54o8 

546  1 

55i5 

5569 

5623 

48 

1  1 

4965 

5O2I 

5o76 

5i3i 

5i86 

5242 

48 

12 

5676 

573o 

5784 

5838 

589i 

5945 

47 

12 

5297 

5353 

54o8 

5463 

55i8 

5574 

47 

i3 

5999 

6o53 

6106 

6160 

6214 

6268 

46 

1  3 

5629 

5684 

574o 

5795 

585o 

5go6 

46 

i4 

632i 

6375 

6429 

6483 

6537 

659o 

45 

i4 

596i 

6016 

6o72 

6127 

6182 

6238 

45 

i5 

6644 

6698 

6752 

6806 

6860 

69i3 

44 

i5 

6293 

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65i5 

657o 

44 

16 

6967 

7021 

7o75 

7129 

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43 

16 

6625 

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6736 

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6847 

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43 

17 

7290 

7344 

7398 

7452 

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42 

17 

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7180 

7235 

42 

18 

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18 

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7568 

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19 

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20 

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39 

20 

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8012 

8068 

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39 

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21 

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38 

22 

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37 

22 

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23 

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24 

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35 

24 

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35 

25 

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34 

25 

9624 

968o 

9735 

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9847 

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34 

26 

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33 

26 

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27 

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28 

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28 

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29 

11  79 

1233 

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29 

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1073 

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1240 

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1612 

1666 

1721 

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29 

3o 

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29 

3i 

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28 

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1687 

1742 

1798 

1  854 

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28 

32 

2i54 

2209 

2263 

2317 

237I 

2426 

27 

32 

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2245 

27 

33 

2480 

2534 

2588 

2643 

2697 

275l 

26 

33 

23oi 

2357 

24i3 

2469 

2525 

258i 

26 

34 

2806 

2860 

2914 

2968 

3o23 

3077 

25 

34 

2636 

2692 

2748 

2804 

2860 

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26 

35 

3i3i 

3i86 

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3294 

3349 

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24 

35 

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3028 

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3i96 

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24 

36 

3457 

35i2 

3566 

3620 

3675 

3729 

23 

36 

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3364 

3420 

3476 

3532 

3588 

23 

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3783 

3838 

3892 

3947 

4ooi 

4o55 

22 

37 

3644 

3700 

3756 

38i2 

3868 

3924 

22 

38 

4no 

4i64 

4219 

4273 

4327 

4382 

21 

38 

398o 

4o36 

4092 

4i48 

4204 

4260 

21 

39 

4436 

449i 

4545 

4599 

4654 

4708 

20 

39 

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4484 

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4596 

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10.324763 

4817 

4872 

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19 

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10.344652 

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4821 

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19 

4i 

5089 

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18 

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52i3 

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42 

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5525 

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5634 

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17 

42 

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5438 

5494 

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5743 

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16 

43 

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16 

44 

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44 

6000 

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6562 

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45 

6337 

6393 

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656a 

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6780 

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6944 

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46 

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6731 

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48 

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7406 

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49 

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7928 

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49 

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9 

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10.348026 

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5i 

8365 

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52 

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52 

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8928 

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53 

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6 

53 

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9098 

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9211 

9267 

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6 

54 

935i 

94o6 

946i 

95i6 

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9625 

5 

54 

938o 

9437 

9493 

955o 

9606 

9663 

5 

55 

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9955 

4 

55 

9719 

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9832 

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.  .  .2 

4 

56 

io.33oooo 

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56 

io.35oo58 

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3 

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2 

57 

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2 

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59 

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O 

60" 

50"  |  40" 

30" 

20" 

10" 

ej 

60" 

50" 

40"  |  30" 

20" 

10" 

c 

Co-tangent  of  25  Degrees. 

Z 

Co-tangent  of  24  Degrees. 

s 

,5  1"  2"  3"  4"  5"  6"  7"  8"  9" 

C  1"  2"  3"  4"  5"  6"  7"  8"  9" 

irll  5  11  1/5  22  27  33  38  43  49 

irt}  6  11  17  22  28  33  39  45  50 

00 


LOGARITHMIC    SINES. 


a 

Sine  of  66  Degrees. 

^c 

Sine  of  67  Degrees. 

9 

0" 

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20" 

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40" 

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20"   30" 

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12 
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52 

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0 

60" 

50" 

40" 

30"   20" 

10" 

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60"     50"  |  40"   30"   20"  |  10" 

Co-sine  of  23  Degrees. 

Co-sine  of  22  Degrees.     s 

.<  1"  2"  3"  4"  5"  6"  7"  8"  9" 
llt  $1234   55   67   8 

.(  1"  -2"  3"  4"  5/;  6"  7"  3"  9" 
irt)  123345678 

LOGARITHMIC    TANGENTS. 


91 


c 

Tangent  of  66  Degrees. 

s 

Tangent  of  67  Degrees. 

2 

0" 

10" 

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2 

57 

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O 

60" 

50"  |  40" 

30"   20" 

10" 

d 

60"    |  50"   40" 

30"   20" 

10" 

• 

Co-tangent  of  23  Degrees. 

% 

Co-  tangent  of  22  Degrees. 

§ 

,(1"  2"  3"  4"  5"  6"  7"  8"  9"  II  p  p  .(  I"  2"  3"  4"  5"  6"  7"  8"  9'' 
lrt{  6  12  17  23  29  35  40  46  52      irt£  6  12  18  24  30  36  42  48  54 

LOGARITHMIC     JSlNES. 


.a 

Sine  of  68  Degrees. 

Jj 

Sine  of  69  Degrees. 

i 

0" 

10" 

20"   30"   40" 

50" 

s 

0" 

10" 

20" 

30" 

40" 

50" 

o 

9.967166 

7174 

7l83  7191  7200 

7208 

59 

o 

9  970152 

0160 

0168 

OI76 

0184 

OI92 

59 

I 

7217 

7225 

72347242  7251 

7259 

58 

I 

O2OO 

0208 

O2l6 

0222 

023: 

0241 

58 

2 

7268 

7276 

7285  7293  7302 

73io 

5? 

2 

O249 

0257 

0265 

027: 

0281 

0289 

57 

c 

7319 

7327 

733673447353 

736i 

56 

r 

0297 

o3o5 

o3i3 

0321 

o329 

o337 

56 

L 

737o 

7378 

73877395  74o4 

7412 

55 

4 

o345 

o353 

o36i 

o37o 

o378 

o386 

55 

i 

742I 

7429 

7437  7446  7454 

7463 

54 

f 

0394 

O4O2 

o4io 

o4i8 

0426 

o434 

54 

6 

747i 

7480 

7488  7497  75o5 

75i4 

53 

6 

0442 

o45o 

o458 

o466 

o474 

0482 

53 

7 

7522 

753i 

7539  7547  7556 

7564 

52 

"3 

0490 

0498 

o5o6 

o5i4 

0522 

o53o 

52 

8 

7573 

758i 

7590  7598  7607 

76i5 

5i 

o538 

o546 

o554 

o562 

o57o 

o578 

5i 

9 

•7624 

7632 

7640  7649  7657 

7666 

5o 

9 

o586 

0594 

o6o2 

0611 

o6i9 

0627 

5o 

10 

9.96767/i 

7683 

7691  7699  7708 

77i6 

49 

10 

9.970635 

o643 

o65i 

o659 

o667 

o675 

49 

ii 

7725 

7733 

774277507758 

7767 

48 

ii 

o683 

0691 

o699 

o7o7 

o7i5 

0723 

48 

12 

7775 

7784 

7792  7801  7809 

78i747 

12 

0731 

o739 

o747 

o755 

o763 

0771 

47 

i3 

•7826 

7834  7843  785i  7859 

7868  46- 

i3 

0779 

0787 

o795 

o8o3 

0811 

o8i9 

46 

i4 

7876 

7885 

7893  7901  7910 

79i845 

i4 

0827 

o835 

0842 

o85o 

o858 

0866 

45 

iS 

7927 

7935 

7943  7952  7960 

7969  44 

i5 

0874 

0882 

o89o 

o898 

o9o6 

o9i4 

44 

16 

7977 

7985 

7994  8002  8011 

8019 

43 

16 

0922 

ogSo 

o938 

o946 

o954 

O962 

43 

17 

8027 

8o36  8o44  8x>53  8061 

8o69 

42 

17 

0970 

0978 

o986 

o994 

1  002 

1010 

42 

18 

8o78 

8086  8094  8io38in 

8120 

4i 

18 

1018 

1026 

io34 

1042 

io5o 

io58 

4i 

'9 

8128 

8i368i458i538i6i 

8i7o 

4o 

19 

1066  1073 

1081 

io89 

io97 

no5 

4o 

20 

9.968i78 

8i87 

8i9582o3 

8212 

8220 

39 

20 

9.971113 

II2I 

II29 

u37 

n45 

n53 

39 

21 

8228 

S245  82538262 

8270 

38 

21 

1161 

1169 

1177 

n85 

iz93 

1  200 

38 

22 

8278 

---/ 

829583o3|83i2 

8320 

37 

22 

1208 

1216 

1224 

1232 

1248 

37 

23 

8329 

8337 

8345,83548362 

83-p 

36 

23 

1256 

1264 

1272 

1280 

1288 

I296 

36 

24 

8379 

8387 

839584o484i2 

8420 

35 

34 

i3o3 

i3n 

i3i9 

I32? 

i335 

1  343 

35 

25 

26 

8429 
8479 

8437  8445|b454  8462 

847o 
8520 

34 
33 

25 

26 

i35i 
i398 

i4o6 

i367 
i4i4 

i375 

i383 
i43o 

i39o 

i438 

34 
33 

27 

8528 

85378545!8553 

8562 

857o 

32 

27 

1  446 

1  4  *>.»  1462 

i469 

1477 

i485 

32 

28 

8578 

8587859586o3 

8612 

8620 

3i 

28 

1493 

i5oi 

i5o9 

i5i7 

i525 

i5323i 

29 

8628 

863686458653866i 

8670 

3o 

29 

i54o 

1  548 

i556 

1  564 

1572 

i58o 

3o 

3o 

9.968678 

86868694|87o387n 

87i9 

29 

3o 

9.971588 

i595 

i6o3 

i6ji 

i6i9 

1627 

29 

3i 

8728 

87368744 

8752 

8761 

8769 

28 

3i 

i635 

i643 

i65i 

i658 

1666 

1674 

28 

32 

8777 

8786  8794 

88028810 

88i9 

27 

32 

1682 

1690 

i698 

I7o6 

I7i3 

1721 

27 

33 

882-7 

8835  8844 

8852  8860 

8868 

26 

33 

1729 

I737 

1745 

i753 

1761 

1768 

26 

34 

8877 

8885  8893 

8901 

8910 

89i8 

25 

34 

1776 

i784 

170.2 

1800 

1808 

i8i5  25 

35 

8926 

8934  8943 

895i 

8959 

8967 

24 

35 

1823 

i83i 

i839 

i847 

i855 

1862124 

36 

8976 

8984 

8992 

9000 

9oo9 

9017 

23 

36 

1870 

i878 

1886 

i894 

I902 

1909  23 

37 

9025 

9033 

9042 

9o5o 

9o58 

9066 

22 

37 

1917 

I925 

i933 

i94i 

I949 

I956  22 

38 

9o75 

9083  9091 

9099 

9io8  9n6 

21 

38 

1964 

I972 

i98o 

i988 

i995 

20O3  21 

39 

9124 

9132  9141 

9149 

9167  9i65 

20 

•39 

201  1 

20I9 

2027 

2o34 

2O42 

2o5o  20 

4o 

9.969173 

9182  9190 

9198 

92069215 

'9 

4o 

9.972O58 

2066 

2073 

2081 

2089 

2097 

i9 

4i 

9223 

923i  9239 

9247 

9256  9264 

18 

4i 

2IO5 

2112 

2120 

2128 

2i36 

2144 

i  a 

42 

9272 

92809288 

9297 

93o5  93i3 

17 

42 

2l5l 

2l59 

2167 

*I75 

2i83 

2I90 

i7 

43 

9321 

93299338 

9346 

93549362 

16 

43 

2198 

22O6  22l4 

2221 

2229 

223? 

16 

44 

937o 

93799387 

9395 

9403,9411 

i5 

44 

2245 

2253 

226O 

2268 

2276 

2284 

i5 

45 

9420 

9428  9436 

9444 

9452|946i 

i4 

45 

2291 

2299 

2307 

23i5 

J322 

233o 

i4 

46 

9469 

94779485 

9493 

gSoi  gSio 

i3 

46 

2338 

2346 

2354 

236i 

2369 

2377 

i3 

47 

95i8 

95269534 

9542 

gSSogSSg 

12 

47 

2385 

2392 

2400 

2408 

2416 

2423 

12 

48 

9567 

95759583 

959i 

9599  9608 

II 

48 

243i 

2439 

2447 

2454 

2462 

2470 

II 

49 

9616 

96249632 

9640 

9648*9657 

10 

49 

2478 

2485 

2493 

25oi 

2  5  08 

25i6 

IO 

5o 

9.969665 

96739681 

9689 

96979705 

9 

5o 

9.972524 

2532 

2539 

2547 

2555 

2563 

9 

5i 

9714 

97229730 

9738 

97469754 

8 

5i 

2570 

2578 

2586 

2593 

2601 

26o9 

8 

52 

9762 

9771  9779 

9787 

979598o3 

7 

52 

2617 

2624 

2632 

2640 

2648  2655 

7 

53 

9811 

98199828 

9836 

9844  9852 

6 

53 

2663 

267I 

2678 

2686 

260,4  2701 

6 

54 

9860 

98689876 

9884 

9893  9901 

5 

54 

2709 

2717 

2725 

2732 

2740 

2748 

5 

55 

9909 

99179925 

9933 

994i  9949 

4 

55 

2755 

2763 

2771 

2778 

2786 

2794 

4 

56 
57 

995799669974 
9.97ooo6  ooi4  0022 

9982 
oo3o 

999°  9998 
oo38  0047 

3 

2 

56 

57 

2802  2809 
2848  2855 

28172825 
2863,2871 

2832 

2878 

2840 
2886 

3 

2 

58    oo55 

oo63  0071 

0079 

0087  oo95 

I 

58 

2894  29OI 

2909  29I7  2924  2932   I 

59 

oio3oiii  0119012701  36  oi  44 

o 

59 

294o  294729552963  2970  20.78  o 

60"     50" 

40"  i  30"   20"   10"  |  e. 

60"    i  50"  :  40"   30"   20"   10"   „. 

Co-sine  of  21  Degrees.     S 

Co-sine  of  20  Degrees. 

f  ^//  2"  3" 

4"  5"  6"  7"  8"  9" 

D  „  .  <  1"  2"  3"  4".  5"  6"  7"  8"  9" 

P.  Part  j  !   o   2 

345677       ul/>  1   2   2   3   4   5   fi   6   7 

LOGARITHMIC    TANGENTS. 


1 

Tangent  of  68  Degrees. 

A 

Tangent  of  69  Degrees. 

X 

0" 

10"  1  20"  |  30" 

40" 

50" 

s 

0" 

10"  |  20" 

30"   40"  |  50" 

o 

i 

10.393590 
3954 

365i 
4oi5 

3712^772 

4o76i4i36 

3833 
4i97 

3894 
4258 

5o 

58 

0 

i 

io.4i5823 
6200 

5886 
6263 

5948 
6326 

6oi  I  6074)6137 

63896452'65i5 

5o 

58 

2 

43i8 

4379 

444o  45oo 

456i 

4622 

57 

t] 

6578 

664i 

6704 

6767 

683o 

6893 

57 

4 

4683 
5o47 

4743 
5io8 

48o4 
5i69 

4865 

5229 

4926 
5290 

&! 

56 
55 

4 

6956 
7335 

7O20 

7398 

7083 
746  1 

7i46 
7524 

7209 

7587 

7272 
765o 

56 
55 

c 

5412 

5473 

5533 

5594 

5655 

57i6 

54 

c 

77i4 

7777 

784o 

79°3 

7966 

8o29 

54 

6 

5777 

5838 

5898 

5959 

6020 

6081 

53 

6 

8o93 

8i56 

82I9 

8282 

8345 

84o9 

53 

7 

6142 

62o3 

6264 

6325 

6385 

6446 

52 

7 

8472 

8535 

8598 

8661 

8725 

8788 

52 

9 

65o7 

6568 

6629 

669o 

675i 

6812 

5i 

885i 

89i4 

8978 

9o4i 

9104 

9i68 

5i 

9 

6873 

6934 

6995 

7o56 

7117 

7178 

5o 

9 

923l 

9294 

9358 

942I 

9484 

9547 

5o 

10 

10.397239 

73oo 

736i 

7422 

7483 

7544 

49 

10 

10.419611 

9674 

9738 

98oi 

9864 

9928 

49 

ii 

7605 

7666 

7727 

7788 

7849 

79io 

48 

II 

9991 

..54 

.118 

.181 

.245 

.3o8 

12 

7971 

8o32 

8o93 

8i54 

82i5 

8276 

47 

12 

I0.42037I 

o435 

0498 

o562 

0625 

o689 

47 

j3 

8337 

8399 

846o 

852i 

8582 

8643 

46 

i3 

O752 

0816 

0879 

o943 

1006 

1070 

46 

i4 

8704 

8765 

8826 

8888 

8949 

9010 

45 

i4 

n33 

n97 

1260 

1324 

i387 

i45i 

45 

i5 

9071 

9l32 

9i94 

9255 

93i6 

9377 

44 

i5 

i5i4 

i578 

i64i 

I7o5 

1769 

i832 

44 

16 

9438 

95oo 

956i 

9622 

9683 

9744 

43 

16 

1896 

i959 

2023 

2086 

2i5o 

22l4 

43 

J7 

9806 

9867 

9928 

9989 

..5! 

.  112 

42 

ll 

2277 

234l 

24o5 

2468 

2532 

2596 

42 

18 

10.400173 

0235 

O296 

o357 

o4i9 

0480 

4i 

18 

2659 

2723 

2787 

285o 

2914 

2978 

4i 

J9 

o54i 

0602 

o664 

0725 

o787 

o848 

4o 

Z9 

3o4i 

3io5 

3i69 

3233 

3296 

336o 

4o 

20 

10.400909 

0971 

1032 

io93 

n55 

1216 

39 

20 

10.423424 

3488 

355; 

36i5 

3679 

3743 

39 

21 

1278 

i339 

i4oo 

1462 

i523 

i585 

38 

21 

38o7 

387o 

3934 

3998 

4062 

4126 

38 

22 

1  646 

1707 

i769 

i83o 

l892 

1953 

37 

22 

4190 

4253 

43i7 

438i 

4445 

45o9 

37 

23 

2Ol5 

2076 

2i38 

2I99 

2261 

2322 

36 

23 

4573 

4637 

4701 

4764 

4828 

4892 

36 

24 

2384 

2445 

2507 

2568 

263o 

2691 

35 

24 

4g56 

502O 

5o84 

5i48 

5212 

5276 

35 

25 

2753 

28i5 

2876 

2938 

2999 

3o6i 

34 

25 

534o 

54o4 

5468 

5532 

5596 

566o 

34 

26 

3l22 

3i84 

3246 

33o7 

3369 

343o 

33 

26 

5724 

5788 

5852 

59i6 

5980 

6o44 

33 

27 

3492 

3554 

36i5 

3677 

3739 

38oo 

32 

27 

6108 

6172 

6236 

63oo 

6364 

6429 

32 

28 

3862 

3924 

3985 

4o47 

4io9 

4170 

3i 

28 

6493 

6557 

6621 

6685 

6749 

68i3 

3i 

29 

4232 

4294 

4356 

44i7 

4479 

454i 

3o 

29 

6877 

694i 

7006 

7o7o 

7i34 

7i98 

3o 

3o 

io.4o46o2 

4664 

4726 

4788 

485o 

4911 

29 

3o 

10.427262 

7327 

739i 

7455 

75i9 

7583 

29 

3i 

4973 

5o35 

5o97 

5i58 

5220 

5282 

28 

3i 

7648 

7712 

7776 

784o 

7905 

7969 

28 

32: 

5344 

54o6 

5468 

5529 

559i 

5653 

27 

32 

8o33 

8o97 

8162 

8226 

8290 

8355 

27 

3$ 

57i5 

5777 

5839 

59oi 

5962 

6024 

26 

33 

84i9 

8483 

8548 

8612 

8676 

8741 

26 

34 

6086 

6i48 

6210 

6272 

6334 

6396 

25 

34 

88o5 

8869 

8934 

8998 

9062 

9I27 

25 

35 

6458 

652O 

6582 

6644 

67o6 

6768 

24 

35 

9191 

9256 

9320 

9384 

9449 

95i3 

24 

36 

6829 

689i 

6953 

7oi5 

7°77 

7i39 

23 

36 

9578 

9642 

97°7 

9771 

9836 

99°° 

23 

3? 

7201 

7263 

7326 

7388 

745o 

75l2 

22 

37 

9965 

.  .29 

..94 

.i58 

.223 

.287 

22 

38 

7574 

7636 

7698 

7760 

•7822 

7884 

21 

38 

io.43o352 

o4i6 

o48i 

o545 

0610 

0674 

21 

39 

7946 

8008 

8070 

8i32 

8i95 

8257 

2O 

39 

°739 

o8o3 

0868 

o933 

0997 

1062 

2O 

4o 

io.4o83i9 

838i 

8443 

85o5 

8567 

863o 

19 

4o 

10.431127 

n9i 

1256 

l32O 

i385 

i45o 

I9 

4i 

8692 

8754 

8816 

8878 

894o 

9003 

18 

4i 

i5i4 

l579 

1  644 

1708 

i773 

i838 

18 

42 

9065 

9127 

9l89 

9252 

93i4 

9376 

ll 

42 

1902 

1967 

2032 

2097 

2161 

2226 

17 

43 

9438 

95oi 

9563 

9625 

9687 

975o 

16 

43 

2291 

2356 

242O 

2485 

255o 

26i5 

16 

44 

9812 

9874 

9937 

9999 

..61 

.123 

i5 

44 

2680 

2744 

28o9 

2874 

2939 

3oo4 

i5 

45 

10.410186 

0248 

o3io 

0373 

o435 

0498 

i4 

45 

3o68 

3i33 

3i98 

3263 

3328 

3393 

i4 

46 

o56o 

0622 

o685 

0747 

0809 

o872 

i3 

46 

3458 

3522 

3587 

3652 

37i7 

3782 

i3 

47 

0934 

0997 

io59 

1122 

1184 

1246 

12 

47 

3847 

39I2 

3977 

4042 

4107 

4172 

12 

48 

i3o9 

i37i 

i434 

i496 

i559 

1621 

II 

48 

4237 

4302 

4367 

4432 

4497 

4562 

II 

49 

1  684 

1746 

i8o9 

1871 

1934 

1996 

IO 

49 

4627 

4692 

4757 

4822 

4887 

4952 

IO 

5o 

10.412059 

2121 

2184 

2246 

2309 

237I 

9 

5o 

10.435017 

5o82 

5i47 

5212 

5277 

5342 

9 

5i 

2434 

2497 

2559 

2622 

2684 

2747 

8 

5i 

5407 

5473 

5538 

56o3 

5668 

5733 

8 

52 

2810 

2872 

2935 

2997 

3o6o 

3i23 

7 

52 

5798 

5863 

5929 

5994 

6o59 

6124 

7 

53 

3i85 

3248 

33u 

3373 

3436 

3499 

6 

53 

6i89 

6254 

6320 

6385 

645o 

65i5 

6 

54 

356i 

3624 

3687 

3749 

38i2 

3875 

5 

54 

658i 

6646 

6711 

6776 

6842 

6907 

5 

55 

3938 

4ooo 

4o63 

4126 

4i89 

425i 

4 

55 

6972 

7o37 

7io3 

7168 

7233 

7299 

4 

56 

43i4 

4377 

444o 

45o2 

4565 

4628 

3 

56 

7364 

7429 

7495 

756o 

7625 

7691 

3 

57 

469i 

4754 

48i7 

4879 

4942 

5oo5 

2 

57 

7756 

7822 

7887 

7952 

8018 

8o83 

2 

58 

5o68 

5i3i 

5i94 

5256 

SSig 

5382 

I 

58 

8i49 

8214 

8279 

8345 

84io 

8476 

I 

59 

5445 

55o8 

5571 

5634 

5697 

576o 

0 

59 

854i 

8607 

8672 

8738 

88o3 

8869 

O 

60" 

50" 

40" 

30" 

20" 

10" 

. 

60" 

50" 

40" 

30" 

20" 

10" 

. 

Co-tangent  of  21  Degrees. 

a 

Co-tangent  of  20  Degrees. 

a 

PPartM"  2"  3"  4"  5//  6"  7"  8//  9" 

.C  1"  2"  3"  4"  5"  6"  7"  8"  9" 

iri$  6  12  19  25  31  37  43  49  56 

in\  6  13  19  26  32  39  45  51  58 

LOGARITHMIC    SINES. 


3 

Sine  of  70  Degrees. 

| 

Sine  of  7  1  Degrees. 

• 

0" 

10" 

20" 

30" 

40" 

50" 

3 

0" 

10" 

20" 

30" 

40" 

50" 

o 

9.972986 

2993 

3ooi 

3oo9 

3oi6 

3o24 

59 

o 

9.975670 

5677 

5685 

5692 

5699 

5706 

59 

I 

3o32 

3o39 

3o47 

3o55 

3o62 

3070 

58 

I 

57i4 

572I 

5728 

5735 

5743 

5750 

58 

2 

3078 

3o85 

3o93 

3ioi 

3io8 

3n6 

57 

2 

5757 

5764 

577i 

5779 

5786 

5793 

57 

3,    3i24 

3i3i 

3i39 

3i46 

3i54 

3i62 

56 

3 

58oo 

58o8 

58i5 

5822 

5829 

5837 

56 

4    8169 

3i77 

3i85 

3i92 

3200 

3208 

55 

4 

5844 

585i 

5858 

5865 

5873 

588o 

55 

5 

32i5 

3223 

323o 

3238 

3246 

3253 

54 

5 

5887 

5894 

59oi 

59o9 

59i6 

5923 

54 

6 

3261 

3269 

3276 

3284 

3291 

3299 

53 

6 

5g3o 

5938 

5945 

5952 

5959 

5966 

53 

7 

3307 

33i4 

3322 

333o 

3337 

3345 

52 

7 

5974 

598i 

5988 

5995 

6002 

6010 

52 

8 

3352 

336o 

3368 

3375 

3383 

3390 

5i 

8 

6oi7 

6024 

6o3i 

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6o46 

6o53 

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9 

3398 

34o6 

34x3 

342i 

3428 

3436 

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9 

6060 

6o67 

6o74 

6081 

6o89 

6096 

5o 

10 

9.973444 

345  1 

3459 

3466 

3474 

3482 

49 

10 

9.976io3 

6110 

6n7 

6i25 

6i32 

6i39 

49 

ii 

3489 

3497 

35o4 

35i2 

35i9 

3527 

48 

ii 

6i46 

6i53 

6160 

6168 

6i75 

6182 

48 

12 

3535 

3542 

355o 

3557 

3565 

3572 

47 

12 

6i89 

6i96 

6203 

6211 

6218 

6225 

47 

i3 

358o 

3588 

3595 

36o3 

36io 

36i8 

46 

i3 

6232 

6239 

6246 

6254 

6261 

6268 

46 

U 

3625 

3633 

364  1 

3648 

3656 

3663 

45 

i4 

6275 

6282 

6289 

6296 

63o4 

63n 

45 

i5 

3671 

3678 

3686 

3694 

3701 

37o9 

44 

i5 

63i8 

6325 

6332 

6339 

6347 

6354 

44 

16 

37i6 

3724 

373i 

3739 

3746 

3754 

43 

16 

636i 

6368 

6375 

6382 

6389 

6396 

43 

17 

376i 

3769 

3777  3784 

3792 

3799 

42 

ll 

64o4 

64ii 

64i8 

6425 

6432 

6439 

42 

18 

3807 

38i4 

3822  3829 

3837 

3844 

4i 

18 

6446 

6454 

646  1 

6468 

6475 

6482 

4i 

J9 

3852 

3859 

3867  3875 

3882 

389o 

4o 

I9 

6489 

6496 

65o3 

65io 

65i8 

6525 

4o 

20 

9.973897 

3905 

3912  3920 

3927 

3935 

39 

20 

9.976532 

6539 

6546 

6553 

656o 

6567 

39 

21 

3942 

SgSo 

3957  3965 

3972 

3980 

38 

21 

6574 

6582 

6589 

6596 

66o3 

6610 

38 

22 

3987 

3995 

4002  4oio 

4oi7 

4o25 

37 

22 

6617 

6624 

663i 

6638 

6646 

6653 

37 

23 

4o32 

4o4o 

4047  4o55 

4062 

4070 

36 

23 

6660 

6667 

6674 

6681 

6688 

6695 

36 

24 

4077 

4o85 

4092  4ioo 

4io7 

4n5 

35 

24 

6702 

67o9 

67i6 

6723 

673i 

6738 

35 

25 

4l22 

4i3o 

4i374i45 

4i52 

4i6o 

34 

25 

6745 

6752 

6759 

6766 

6773 

6780 

34 

26 

4l67 

4i75 

4182  4190 

4i97 

42o5 

33 

26 

6787 

6794 

6801 

6808 

68i5 

6823 

33 

27 

4212 

4220 

42274235 

4242 

425o 

32 

27 

683o 

6837 

6844 

685i 

6858 

6865 

32 

28 

4257 

4264 

42724279 

428-7 

4294 

3i 

28 

6872 

6879 

6886 

6893 

69oo 

6907 

3r 

29 

3o 

43o2 
9*974347 

43o9 
4354 

43i74324 
436i4369 

4332 
4376 

4339 
4384 

3o 
29 

o9 

3o 

69i4 
9.976957 

692I 

6964 

6928 
697i 

6935 
6978 

6942 
6985 

6950 
6992 

3o 
29 

3i 

439i 

4399 

44o644r4 

442i 

4428 

28 

3i 

6999 

7006 

7oi3 

7020 

7027 

7o34 

28 

32 

4436 

4443 

445i  4458 

4466 

44?3 

27 

32 

7o4i 

7o48 

7o55 

7062 

7o69 

7076 

27 

33 

448  1 

4488 

4495  45o3 

45io 

45i8 

26 

33 

7o83 

7090 

7°97 

7104 

7ni 

7118 

26 

34 

4525 

4533 

454o4547 

4555 

4562 

25 

34 

7i25 

7132 

7i39 

7i46 

7i53 

7160 

25 

35 

457o 

4577 

45854509 

4599 

4607 

24 

35 

7167 

7174 

7181 

7188 

•7195 

7202 

24 

36 

46i4 

4622 

4629  4636 

4644 

465i 

23 

36 

7209 

7216 

7223 

7230 

7237 

7244 

23 

37 

4659 

4666 

46744681 

4688 

4696 

22 

37 

725l 

7258 

7265 

7272 

7279 

7286 

22 

38 

4?o3 

47n 

47184725 

4733 

474o 

21 

38 

7293 

73oo 

73o7 

73x4 

732I 

7328 

21 

39 

4748 

4755 

4762477° 

4777 

4784 

2O 

39 

7335 

7342 

7349 

7356 

7363 

737o 

20 

4o 

9.974792 

4799 

48o748i4 

4821 

4829 

19 

4o 

9.977377 

7384 

739i 

7398 

74o5 

7412 

J9 

4i 

4836 

4844 

485i  4858 

4866 

4873 

18 

4i 

74i9 

7426 

7433 

744o 

7447 

7454 

18 

4a 

488o 

4888 

48954903 

4910 

4917 

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42 

746  1 

7468 

7475 

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7489 

7496 

17 

43 

•4925 

4932 

49394947 

4954 

4961 

16 

43 

75o3 

75io 

75i7 

7524 

753o 

7537 

16 

44 

4969 

4976 

49844991 

4998 

5oo6 

i5 

44 

7544 

755i 

7558 

7565 

7572 

7579 

i5 

45 

5oi3 

5020 

5o28;5o35 

5o42 

5o5o 

i4 

45 

7586 

7593 

7600 

76o7 

7614 

7621 

i4 

46 

5o57 

5o64 

5072^079  5o86 

5094 

i3 

46 

7628 

7635 

7642 

7648 

7655 

7662 

i3 

47 

5ioi 

5io8 

5u6  5i23  5i3o 

5i38 

12 

47 

7669 

7676 

7683 

769o 

7697 

77°4 

12 

48 

5i45 

5i52 

5i6o  5167 

5i74 

5i82 

II 

48 

7711 

7718 

7725 

7732 

7739 

7745 

II 

49 

5i89 

5196 

5204  5211 

52i8 

5226 

10 

49 

7752 

7759 

7766 

7773 

7780 

7787 

10 

509.975233 

524o 

524852555262 

5270 

9 

5o 

9-977794 

7801 

7808 

78i5 

7821 

7828 

9 

5i 

5277 

5284 

5292  5299(5306 

53i3 

8 

5i 

7835 

7842 

7849 

7856 

7863 

7870 

8 

52 

532i 

5328 

5335  5343  535o 

5357 

7 

52 

7877 

7884 

7890 

7897 

79°4 

7911 

7 

53    5365 

5372 

5379  5386  5394 

54oi 

6 

53 

79i8 

7925 

7932 

7939 

7946 

7952 

6 

541    54o8 

54i6 

5423 

543o5437 

5445 

5 

54 

7959 

7966 

7973  798° 

7987 

7994 

5 

55:    5452 

5459 

5467 

5474548i 

5488 

4 

55 

8001 

8oo7 

8oi4!8o2i  8028 

8o35 

4 

56    5496 

55o3 

55io 

55i8,5525 

5532 

3 

56 

8042 

8o498o56  8o62|8o69 

8o76 

3 

57    5539 

5547 

5554 

556i'5568 

5576 

2 

57 

8o83 

8o9o  8o97l8io4  81  10 

8117 

2 

58 

5583 

559o 

5598 

56o556i2 

56i9 

I 

58 

8i248r3r8i38 

8i45!8i52 

8i58 

I 

59 

5627 

5634 

564i 

56485656 

5663 

O 

59 

8i65  81728179 

818681938199 

O 

60" 

50" 

40" 

30"   20" 

10" 

c 

60"    j  50"   40"  j  30"   20"  |  10" 

a 

Co-sine  of  19  Degrees. 

ii 

Co-sine  of  1  8  Degrees. 

1 

pp  .C  1"  2"  3"  4"  5"  6"  7"  8"  9" 
irt$  1   123   44567 

P  T»  ^  l';  2"  3"  4"  5"  6"  7"  <~ 
trt{  1   1   2   3   4   4   3   ft   6 

LOGARITHMIC    TANGENTS 


95 


d 

Tangent  of  70  Degrees. 

d 

Tangent  of  7  1  Degrees. 

s 

0" 

10" 

20" 

ao" 

40" 

50" 

s 

0" 

10" 

20" 

30" 

40" 

5<y 

o 

o.438934 

9ooo 

9o65 

9i3i 

9196 

9262 

59 

0 

io.463o28 

3097 

3i65 

3233 

33o2 

3370 

59 

I 

9327 

9393 

9458 

95a4 

959o 

9655 

58 

I 

3439 

3507 

3576 

3644 

37i3 

378i 

58 

2 

3 

•   9721 
o  .  44o  i  i  5 

9786 
0180 

9852 
0246 

9918 

0312 

9983 
o377 

.49 

o443 

56 

2 

3 

*   385o 
4261 

39i8 
4329 

3987 
4398 

4o55 
4466 

4124 
4535 

4i92|57 
46o4!56 

4" 

0509 

o574 

o64o 

0706 

o77i 

o837 

55 

4 

4672 

4-74-  i 

48o9 

4878 

4947 

5oi5 

55 

5 

0903 

o969 

io34 

IIOO 

166 

1232 

54 

5 

5o84 

5i53 

5221 

)29O 

5359 

5427 

54 

6 

1297 

i363 

i42^b 

1495 

56i 

1627 

53 

6 

5496 

5565 

5633 

57O2 

577i 

584o 

53 

7 

1692 

i758 

1824 

1890 

956 

2O22 

52 

7 

59o8 

5977 

6o46 

6n5 

6184 

6252 

02 

8 

2087 

2i53 

22I9 

2285 

235i 

24l7 

5i 

8 

632i 

6459 

6528 

6596 

6665 

5i 

9 

2483 

2549 

26l5 

2681 

2747 

28l3 

5o 

9 

6734 

68o3 

6872 

694i 

7030 

7079 

5o 

10 

0.442879 

2945 

3oii 

3o77 

3i43 

32O9 

49 

10 

10.467147 

•7216 

7285 

7354 

7423 

7492 

49 

ii 

3275 

334i 

3407 

3473 

|539 

36o5 

48 

ii 

756i 

763o 

7699 

7768 

7837 

7906 

48 

12 

3671 

3737 

38o3 

3869 

iooi 

47 

12 

7975 

8o44 

8n3 

8182 

825i 

8320 

47 

i3 

4067 

4i33 

4200 

4266 

i332 

4398 

46 

i3 

.   8389 

8458 

8527 

8597 

8666 

8735 

46 

i4 

4464 

453o 

i596 

4663 

4729 

4?95 

45 

:4 

88o4 

8873 

8942 

9on 

9o8o 

9i5o 

45 

i5 

486i 

4927 

4994 

5o6o 

5i26 

5192 

44 

i5 

9219 

9288 

9357 

9426 

9496 

9565 

44 

16 

5259 

5325 

539i 

5457 

5524 

SSgo 

43 

16 

9634 

97°3 

9772 

9842 

99" 

998o 

43 

ll 

5656 

5722 

5789 

5855 

592I 

5988 

\z 

i7 

io.47oo49 

0119 

0188 

0257 

0327 

o396 

ia 

18 

6o54 

6120 

6i87 

6253 

6320 

6386 

\i 

18 

o465 

o535 

o6o4 

0673 

o743 

0812 

ii 

*9 

6452 

65i9 

6585 

6652 

6718 

6784 

4o 

!9 

0881 

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IO2O 

IO9O 

u59 

1228 

io 

20 

o.44685i 

6917 

6984 

7o5o 

7117 

7i83 

39 

20 

10.471298 

i367 

i437 

i5o6 

i576 

1  645 

39 

21 

725o 

73i6 

7383 

7449 

75i6 

7582 

38 

21 

1715 

i784 

i854 

1923 

i993 

2062 

38 

22 

?649 

77i5 

7782 

7848 

7915 

7981 

37 

22 

2l32 

22OI 

2271 

234o 

2410 

2480 

37 

23 

8n5 

8181 

8248 

83i4 

838i 

36 

23 

2549 

2619 

2688 

2758 

2828 

2897 

36 

24 

8448 

85i4 

858i 

864? 

8714 

8781 

35 

24 

2967 

3o37 

3io6 

3i76 

3246 

33i5 

35 

25 

8847 

8914 

898i 

9o48 

9114 

9181 

34 

25 

3385 

3455 

3524 

3594 

3664 

3734 

34 

26 

9248 

93i4 

938i 

9448 

95i5 

958i 

33 

26 

38o3 

3873 

3943 

4oi3 

4082 

4i52 

33 

27 

9648 

97i5 

9782 

9848 

9915 

9982 

32 

27 

4222 

4292 

4362 

4432 

45oi 

4571 

32 

28 

io.45oo49 

0116 

oi83 

0249 

o3i6 

o383 

3i 

28 

464i 

47" 

4?8i 

485i 

4921 

4991 

3i 

29 

o45o 

o5i7 

o584 

o65i 

0717 

0784 

3o 

29 

5o6o 

5i3o 

52OO 

527O 

534o 

54io 

3d 

3o 

io.'45o85i 

o9i8 

o985 

1052 

1119 

1186 

29 

3o 

10.475480 

555o 

5620 

5690 

5760 

583o 

29 

3i 

1253 

1320 

i387 

i454 

1521 

i588 

28 

3i 

5900 

5970 

6o4o 

6no 

6180 

625o 

28 

32 

i655 

1722 

1789 

i856 

1923 

1990 

27 

32 

63ao 

639r 

646i 

653i 

6601 

6671 

27 

33 

2057 

2124 

2191 

2258 

2325 

2392 

26 

33 

674i 

68  1  1 

6881 

6952 

7022 

7092 

26 

34 

2460 

2527 

2594 

2661 

2728 

2795 

25 

34 

7162 

7232 

7302 

7373 

7443 

75i3 

25 

35 

2862 

2929 

2997 

3o64 

3i3i 

3198 

24 

35 

7583 

7654 

7724 

7794 

7864 

7935 

24 

36 

3265 

3333 

34oo 

3467 

3534 

3602 

23 

36 

8oo5 

8o75 

8i46 

8216 

8286 

8357 

23 

37 

3669 

3736 

38o3 

3871 

3938 

4oo5 

22 

37 

8427 

8497 

8568 

8638 

8708 

8779 

22 

38 

4072 

4i4o 

4207 

4274 

4342 

4409 

21 

38 

8849 

892O 

899o 

9061 

9i3i 

9201 

21 

39 

4476 

4544 

46n 

4678 

4746 

48i3 

2O 

39 

9272 

9342 

94i3 

9483 

9554 

9624 

2O 

4o 

io.45488i 

4948 

5oi5 

5o83 

5i5o 

6218 

19 

4o 

10.479695 

9765 

9836 

9906 

9977 

»  .47 

19 

4i 

5285 

5353 

5420 

5488 

5555 

5623 

18 

4i 

10.480118 

0189 

0259 

o33o 

o4oo 

0471 

18 

42 

569o 

5758 

5825 

5893 

5960 

6028 

17 

42 

o542 

0612 

o683 

o754 

0824 

o895 

17 

43 

6o95 

6i63 

623o 

6298 

§365 

6433 

16 

43 

0966 

io36 

1107 

1178 

1248 

i3i9 

16 

44 

65oi 

6568 

6636 

670^ 

6771 

6839 

i5 

44 

1390 

i46i 

i53i 

1602 

i673 

1744 

i5 

45 

69o6 

6974 

7042 

7109 

7177 

7245 

i4 

45 

1814 

i885 

i956 

2O27 

2098 

2i69 

i4 

46 

73l2 

738o 

7448 

7583 

765i 

i3 

46 

2239 

23lO 

238i 

2452 

252^ 

2594 

i3 

47 

77i9 

7786 

7854 

7922 

799° 

8o57 

12 

47 

2665 

2736 

2807 

2877 

2948 

3oi9 

12' 

48 

8i25 

8i93 

8261 

8329 

8397 

8464 

II 

48 

Sogo 

3i6i 

3232 

33o3 

3374 

3445 

ii 

49 

8532 

8600 

8668 

8736 

88o4 

8872 

10 

49 

35i6 

3587 

3658 

3729 

38oo 

387i 

IO 

5o 

10.458939 

9oo7 

9°75 

9i43 

92II 

9279 

9 

5o 

10.483943 

4oi4 

4o85 

4i56 

4227 

4298 

9 

5i 

934? 

94i5 

9483 

955i 

9619 

9687 

8 

5i 

4369 

444o 

45n 

4583 

4654 

4725 

8 

52 

9755 

0823 

9891 

9959 

.  .27 

..95 

"J 

52 

4796 

4867 

4938 

5oio 

5o8i 

5i52 

7 

53 

10.46016!: 

023l 

0299 

0367 

0435 

o5o; 

53 

5223 

5295 

5366 

5437 

55o8 

558o 

6 

54 

©571 

o639 

0707 

0776 

0844 

0912 

K 

54 

565i 

5722 

5794 

5865 

5936 

6008 

5 

55 

o98o 

io48 

1116 

n84 

1253 

l32I 

4 

55 

6o79 

6i5o 

6222 

629. 

636; 

6436 

4 

56 

i389 

i457 

i525 

i5g^ 

1662 

I73o 

1 

56 

65o7 

6579 

665o 

6722 

6793 

6864 

3 

^7 

1798 

1867 

i935 

200' 

2071 

2 

57 

6936 

7007 

7°79 

7i5o 

7222 

7293 

2 

58 

2208 

2276 

2345 

24l3 

2481 

255o 

I 

58 

7365 

7436 

75o8 

758o 

765i 

7723 

I 

59 

2618 

2686 

2755 

2823 

2891 

2960 

O 

59 

7794  7866  7937 

8oo9 

8081 

8i52 

O 

60" 

50"   40" 

30" 

20" 

10" 

S" 

60"     50"   40"   30" 

20" 

10" 

g' 

Co-tangent  of  19  Degrees. 

Co-tangent  of  18  Degrees. 

.  <  1"  2"  3"  4"  5"  6"  7"  8"  9" 

<  1"  2"  3"  4"  5"  6"  7"  8"  9" 

llt\  7  13  20  27  33  40  47  54  60 

;  '  art}  7  14  21  28  35  42  49  56  63 

LOGARITHMIC    SINEB. 


.s 

Sine  of  72  Degrees. 

-' 

Sine  of  73  Degrees. 

m 

0" 

10" 

20"   30"  |  40" 

50" 

0" 

10" 

20" 

30"  |  40" 

50" 

c 

9.9782o6  82i3 

822082278234 

824l 

69 

0 

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8247  8264  8261,8268  8275  8282 

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2      8288:8296 

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2 

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55 

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9.9786i5j8622!86288635 
8655  8662  8669'8676 

8642 
8682 

8649 
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49 

48 

10 

ii 

9.980981 
1019 

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1026 

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48 

2 

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12 

1067 

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1070 

1076 

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1089 

47 

V 

8737 

8743:87608767 

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46 

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1096 

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1  1  20 

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879i  8797 

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8811 

45 

li 

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8861 

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jf 

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1177 

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44 

16 

8858 

8865 

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43 

16 

1209 

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1222 

1228 

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1241 

43 

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8898 

8906 

89i2  89i8l8925 

8932 

42 

17 

I247 

1253 

1260 

1266 

1272 

1279 

42 

18 
19 

8939 
8979 

8946  8962  896918^65  8972 
8986  8992  8999|9oo6  9oi2 

4i 

4o 

18 
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1286 
i323 

1291 
1329 

1298 

i336 

i3o4 

1  342 

i3io 
1  348 

i3i7 
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4o 

20 

9.979019 

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39 

20 

9.98i36i 

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i373 

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1392 

39 

21 

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9o66  9073 

9679 

9o86 

9o93 

38 

21 

i399 

i4o5 

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1424 

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38 

22 

9100 

9106  9113 

9120 

9I26 

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37 

22 

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1  449 

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1  468 

37 

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9140 

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9i66 

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23 

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36 

25 

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9186  9193  9200 
9227  9233  9240 

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35 
34 

24 

25 

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1649 

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1624 
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1668 

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35 

34 

26 

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33 

26 

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1606 

1612 

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33 

27 

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93069313 

9320 

9326 

9333 

32 

27 

1626 

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i637 

1  643 

1660 

1666 

32 

28 

934o 

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9360 

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3i 

28 

1662 

1668 

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1687 

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3i 

29 

938o 

93869393 

9400 

9406  94i3 

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29 

I7OO 

1706 

I7I2 

1718 

1724 

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3o 

3o 

9.979420 

9426  9433 

9439 

9446 

9453 

29 

3o 

9  98i737 

1743 

i749 

1766 

1762 

i768 

29 

3i 

9459 

9466  9473 

9479 

9486  9492 

28 

3i 

i774 

1781 

1787 

1793 

1799 

1806 

28 

32 

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96069612 

9619  9526  9532 

27 

32 

18:2 

1818 

1824 

i83o  1837 

i843 

27 

33 

34 

9539 
9679 

9545  9662 
9686  9592 

9559 
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966619672 
96o5'96i2 

26 

25 

33 

34 

1849 
1886 

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i893 

1861 
1899 

1868 
1906 

1874 
1911 

1880 
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26 
25 

35 

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9638 

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24 

35 

1924 

i93o 

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1942 

1  9<48 

1966 

24 

36 

9668 

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9678 

9684  9691 

23 

36 

1961 

1967 

i973 

1979 

1986 

1992 

23 

37 

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9717 

97249730 

22 

37 

1998 

20O4 

20IO 

2016 

12023 

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22 

38 

9737 

9743  9760 

9767 

97639770 

21 

38 

2o35 

2041 

2047 

2O6O 

2066 

21 

39 

9776 

97839790 

9796 

9803  9809 

2O 

39 

2072 

2078 

2084 

2091 

2097 

2103 

2O 

4o 
4i 

9.979816 
9866 

9822  9829 
9862  9868 

9836 
9876 

98429849 
9881  9888 

Is 

4o 
4i 

9.982109 
2146 

2Il5 
2152 

2122 
2169 

2128 
2i65 

2  I  34 
2171 

2140 
2I77 

19 

18 

42 

9896 

9901  9908 

99i4 

9921  9927 

17 

42 

2i83 

2189  2196 

22O2 

2208 

22  1  4 

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43 

9934 

9940  9947 

9964 

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16 

43 

222O 

2226  2232 

2239 

2245  2125  I 

16 

44 

9973 

9980  9986 

9993 

9999  ...6 

16 

44 

2257 

2263 

2269 

2276 

2282 

2288 

16 

45 

9.980012 

00190026 

OO32 

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i4 

45 

2294 

2300 

23o6 

23l2 

23i82324 

i4 

46 

0062 

00680066 

6071 

0078  0084 

i3 

46 

2331 

2337 

2343 

2349 

2355 

236i 

i3 

47 

0091 

0097  0104 

OIIO 

0117  0123 

12 

47 

2367 

2373 

238o 

2386 

2392 

2398 

12 

48 

oi3o 

oi36oi43 

oi49 

0166  oi63 

II 

48 

2404 

2410 

2416 

2422 

2429 

2435 

II 

49 

0169 

0176  0182 

oi89 

0196  0202 

IO 

49 

244  1 

2447 

2453 

2469 

2465 

247I 

IO 

5o 

9.980208 

02l5  0221 

0228 

02340241 

9 

5o 

9.982477 

2484 

2490 

2496 

2602 

2608 

9 

5i 

0247 

0254  0260 

0267 

0273  0280 

8 

5i 

2614 

2620 

2626 

2532 

2538 

2544 

8 

62 

0286 

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o3o6 

o3i2o3i8 

7 

62 

2661 

2667 

2563 

2669 

2676 

2681 

7 

53 

o325 

o33i  o338 

o344 

o35i'o357 

6 

53 

2587 

2693 

2699 

2606 

261  1 

2617 

6 

54 

o364 

08700377 

o383 

0390  0396 

5 

54 

2624  263o 

2636 

2642 

2648 

2664 

5 

55 

o4o3 

o4o9  o4i6 

0422 

0429  0435 

4 

55 

2660  2666  2672 

2678 

2684 

2690 

4 

56 

o48o 

o448o454 
o487o493 

o46i 
0600 

0467  o474 
o5o6o5i3 

3 

2 

56 

57 

2696J27O2  2709 

2733  2739  2745 

271612721 
276112757 

2727 
2763 

3 

2 

58 

o5"i9 

06260632 

o538 

o545  0661 

I 

58 

2769  2775  278i 

2787'27932799  i 

59 

0668 

o564  0671 

0677 

06830690 

O 

69 

2806  28ii!28i7|2824  28302836  o 

60" 

50-  | 

40"   30"   20"   10" 

ri 

60"  ^  i  50"   40"   30"   20"   10-   ^ 

Co-sine  of  17  Degrees. 

Co-sine  of  16  Degrees. 

f  j//  g//  g// 

4"  5"  6"  7"  8"  9"   p  p  .(!"  2"  3"  4"  5"  6"  7"  8'  9" 

(1   12 

3   3   4  5   5   6  :  r'rarM  1   12234436 

LOGARITHM    c    TANGENTS. 


4 

Tangent  of  7  ^  Decrees. 

d 

Tangent  of  73  Degrees. 

s 

0" 

10" 

20" 

30"  |  40"J  50"  | 

i 

0" 

10" 

20" 

30" 

40" 

50" 

o 

10.488224 

8296 

8367 

8439 

85n 

8582 

5o 

0 

io.5i466i 

4736 

4812 

4887 

4962 

5o38 

59 

I 

8654 

8726 

8797 

8869 

894i 

9oi3 

58 

I 

5n3 

5i88 

5264 

5339 

54i5 

549o 

58 

2 

9084 

9i56 

9228 

93oo 

937i 

9443 

57 

2 

5565 

564i 

57i6 

5792 

5867 

5943 

5? 

3 

95i5 

9587 

9659 

973i 

9802 

9874 

56 

3 

6018 

6094 

6i69 

6245 

6320 

6396 

56 

4 

9946 

..18 

..90 

.162 

.-234 

.3o6 

55 

4 

6471 

6547 

6623 

6698 

6774 

6849 

55 

5 

io.^9o378 

o449 

0521 

o593 

o665 

o737 

54 

5 

6925 

7OOI 

7o76 

7l52 

7228 

73o3 

54 

6 

0809 

0881 

0953 

IO25 

io97 

n69 

53 

6 

7379 

7455 

753o 

76o6 

7682 

7758 

53 

7 

1241 

i3i3 

i386 

i458 

i53o 

1602 

52 

7 

7833 

79°9 

7985 

8061 

8i37 

8212 

52 

8 

i674 

i746 

1818 

1890 

I962 

2o35 

5i 

8 

8288 

8364  844o 

85i6 

8592 

8667 

5i 

9 

2107 

2I79 

225l 

2323 

2395 

2468 

5o 

9 

8743 

8819 

8895 

8971 

9o47 

9I23 

5o 

10 

10.492540 

2612 

2684 

2757 

2829 

29OI 

A9 

10 

io.5i9i99 

9275 

935i 

9427 

95o3 

9579 

49 

ii 

2973 

3o46 

3n8 

3190 

3263 

3335 

48 

n 

9655 

973i 

98o7 

9883 

9959 

..35 

48 

12 

34o7 

348o 

3552 

3624 

3697 

3769 

47 

12 

IO.520III 

oi87 

0263 

o34o 

o4i6 

O492 

47 

i3 

384i  39i4 

3986 

4o59 

4i3i 

4204 

46 

i3 

o568 

o644 

0720 

o797 

o873 

o949 

46 

i4 

4270,4348 

442i 

4493 

4566 

4638 

45 

r4 

IO25 

IIOI 

1178 

ia54 

i33o 

i4o7 

45 

i5 

47ir:4783 

4856 

4928 

5ooi 

5o74 

44 

r5 

i483 

i559 

i635 

I7I2 

1788 

1864 

44 

16 

5i46 

52I9 

5291 

5364 

5437 

55o9 

43 

16 

i94i 

20I7 

2094 

2I70 

2246 

2323 

43 

X7 

5582 

5654 

5727 

58oo 

5872 

5945 

42 

*7 

2399 

2476 

2552 

2628 

27o5 

278l 

42 

18 

6018 

6o9o 

6i63 

6236 

63o9 

638i 

4i 

18 

2858 

2934 

3on 

3o87 

3i64 

324i 

4i 

J9 

6454 

6527 

6600 

6672 

6745 

6818 

4o 

X9 

33i7 

3394 

3470 

3547 

3623 

37oo 

4o 

20 

10.496891 

6964 

7o36 

7I09 

7l82 

7255 

39 

20 

io.523777 

3853 

393o 

4oo7 

4o83 

4i6o 

39 

21 

7328 

74oi 

7474 

7547 

76i9 

6792 

38 

21 

4237 

43i3 

439o 

4467 

4544 

4620 

38 

22 

7765 

7838 

7911 

7984 

8o57 

8i3o 

37 

22 

4697 

4774 

485i 

4927 

5oo4 

5o8i 

37 

23 

82o3 

8276 

8349 

8422 

8495 

8568 

36 

23 

5i58 

5235 

53i2 

5388 

5465 

5542 

36 

24 

864i 

87i4 

8787 

8860 

8934 

9oo7 

35 

24 

56i9 

5696 

5773 

585o 

5927 

6oo4 

35 

25 

9080 

9i53 

9226 

9299 

9372 

9445 

34 

25 

6081 

6i58 

6235 

63i2 

6389 

6466 

34 

26 

9519 

9592 

9665 

9738 

9811 

9885 

33 

26 

6543 

6620 

6697 

6774 

685i 

6928 

33 

27 

9958 

.  .3i 

.104 

.i78 

.261 

.324 

32 

27 

7oo5 

•7082 

7160 

7237 

73i4 

739i 

32 

28 

io.5oo397 

o47i 

o544 

06  1  7 

0691 

o764 

3i 

28 

7468 

7545 

7623 

77oo 

7777 

7854 

3i 

'29 

0837 

o9n 

0984 

io57 

n3i 

I2O4 

3o 

29 

793i 

8oo9 

8086 

8i63 

8241 

83i8 

3o 

3o 

10.501278 

i35i 

1425 

1498 

i57i 

1645 

29 

3o 

10.528395 

8472 

855o 

8627 

87o5 

8782 

29 

3i 

1718 

I792 

i865 

i939 

2OI2 

2086 

28 

3i 

8859 

8937 

9oi4 

9o9i 

9l69 

9246 

28 

32 

2l59 

2233 

23o7 

238o 

2454 

2527 

27 

32 

9324 

94oi 

9479 

9556 

9634 

9711 

27 

33 

2601 

2674 

2748 

2822 

2895 

2969 

26 

33 

9789 

9866 

9944 

.  .21 

••99 

.177 

26 

34 

3o43 

3u6 

3190 

3264 

3337 

34n 

25 

34 

io.53o254 

o332 

o4o9 

o487 

o565 

0642 

25 

35 

3485 

3559 

3632 

37o6 

378o 

3854 

24 

35 

0720 

o798 

o875 

o953 

io3i 

1108 

24 

36 

3927 

4ooi 

4o75 

4i49 

4223 

4296 

23 

36 

1186 

1264 

1  342 

i4i9 

*497 

i575 

23 

37 

4370 

4444 

45i8 

4592 

4666 

474o 

22 

37 

i653 

I73i 

1808 

1886 

1964 

2042 

22. 

38 

48i4 

4887 

4961 

5o35 

5  1  09 

5i83 

21 

38 

2120 

2I98 

2276 

2353 

243l 

25o9 

21 

39 

5257 

533i 

54o5 

5479 

5553 

5627 

20 

39 

2587 

2665 

2743 

2821 

2899 

3977 

2O 

4o 

io.5o57oi 

5775 

5849 

5923 

5997 

6o7i 

I9 

4o 

io.533o55 

3i33 

3211 

3289 

3367 

3445 

*9 

4i 

6i46 

6220 

6a94 

6368 

6442 

65i6 

18 

4i 

3523 

36o2 

368o 

3758 

3836 

39i4 

18 

42 

659o 

6664 

6739 

68i3 

6887 

696i 

17 

42 

3992 

4o7o 

4i49 

4227 

43o5 

4383 

i? 

43 

7o35 

7no 

7i84 

7258 

7332 

74o7 

16 

43 

446i 

454o 

46i8 

4696 

4774 

4853 

16 

44 

748i 

7555 

763o 

77o4 

7778 

7853 

i5 

44 

493i 

5oo9 

5o88 

5i66 

5244 

5323 

i5 

45 

7927 

8001 

80-76 

8i5o 

8224 

8299 

i4 

45 

54oi 

5479 

5558 

5636 

57i5 

5793 

i4 

46 

8373 

8448 

8522 

8596 

8671 

8745 

i3 

46 

5872 

595o 

6028 

6io7 

6i85 

6264 

i3 

47 

8820 

8894 

8969 

9o43 

9118 

9I92 

12 

47 

6342 

6421 

6499 

6578 

6657 

6735 

12 

48 

9267 

934i 

94i6 

949o 

9565 

964o 

II 

48 

68i4 

6892 

697i 

7o5o 

7I28 

7207 

II 

49 

97i4 

9789 

9863 

9938 

..i3 

..87 

10 

49 

7285 

7364 

7443 

7522 

76oo 

7679 

10 

5o 

io.5ioi62 

0237 

o3ii 

o386 

o46i 

o535 

9 

5o 

io.537758 

7836 

79i5 

7994 

8o73 

8i5i 

9 

Si 

0610 

o685 

o76o 

o834 

o9o9 

o984 

8 

5i 

823o 

83o9 

8388 

8467 

8546 

8624 

8 

52 

io59 

n34 

1208 

1283 

i358 

i433 

7 

52 

87o3 

8782 

8861 

894o 

9OI9 

9o98 

7 

53 

i5o8 

i582 

i657 

I732 

1807 

1882 

6 

53 

9i77 

9256 

9335 

94i4 

9493 

9572 

6 

54 

i957 

2032 

2IO7 

2182 

2257 

2332 

5 

54 

965i 

973o 

98o9 

9888 

9967 

..46 

5 

55 

2407 

2482 

2557 

2632 

2707 

2782 

4 

55 

io.54pi25 

O204 

0283 

o362 

0442 

0521 

4 

56 

2857 

2932 

3oo7 

3082 

3i57 

3232 

3 

56 

0600 

o679 

o758 

o837 

°9I7 

o996 

3 

57 

3307 

3382 

3457 

3533 

36o8 

3683 

2 

57 

io75 

n54 

1234 

i3i3 

I392 

l472 

2 

58 

3758 

3833 

39o8 

3984 

4o59 

4i34 

I 

58 

i55i 

i63o 

I7IO 

i789 

1868 

i948 

I 

59 

42O9 

4285 

436o 

4435 

45io 

4586 

O 

59 

2027 

2106 

2186 

2265 

2345 

2424 

O 

60" 

50" 

40" 

30" 

20" 

10" 

g 

60" 

50" 

40" 

30" 

20" 

10" 

j 

Co-  tangent  of  17  Degrees. 

Co-tangent  of  16  Degrees. 

§ 

p  p  .$  1"  2"  3"  4"  5"  6"  7"  8"  9" 
I  7  15  22  29  37  44  51  59  66 

p  p  t  f  1"  2"  3"  4"  5"  6"  7"  8"  9" 
in\  8  15  23  31  39  46  54  62  70 

98 


LOGARITHMIC    SINES. 


.9 

Sine  of  74  Degrees. 

a 

Sine  of  75  Degrees. 

s 

0" 

10" 

20" 

30"  1  W 

50* 

3     0"     10" 

20" 

30" 

40" 

50" 

o 

9.98a842  2848 

2854286o|2866 

2872  59 

0 

9.9849444949 

49bb 

4961 

4966 

4972 

59 

I 

2878  2884 

2890 

2896,29O2 

2908  58 

I 

49784983 

498o 

4995 

5ooo 

5oo6 

58 

2 

2914 

2920 

2926 

2932  2938 

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2 

5on  5oi7 

5o23 

5028 

5o34 

5o4o 

57 

3 

2g5o 

2956 

2962  296812974 

2980  56 

3 

5o45  5o5i 

5o56 

5o62 

5o68 

5o73 

56 

4 

298612992 

2998 

3oo4i3oio 

3oi655 

4 

5o79  5o84 

5090 

5o96 

5ioi 

5io7 

55 

5 

3022  3028 

3o34 

3o4o3o46 

3o52  54 

5 

5n3 

5n8 

5i24 

5129 

5i35 

5i4i 

54 

6 

3o58 

3o64 

3o7o  3o76;3o82 

3o88  53 

6 

5i46 

5i52 

5i57 

5i63 

5i69 

5i74 

53 

7 

3094 

3ioo 

3io6 

3lI2  ;3ll8 

312452 

7 

5i8o 

5i85 

5191 

5i97 

52O2 

5208 

52 

8 

3i3o 

3i36 

3i42 

3i483i54 

3i6o!5i 

8 

52i3 

5219 

5224 

523o 

5236 

524i 

5i 

9 

3i66 

3l72 

3i78 

3i84 

3190 

3i96|5o 

9 

5247 

5252 

5258 

5264 

5269 

5275 

5o 

10 

5,983202 

3208- 

32l4 

3220 

3226 

323249 

10 

$.985280 

5286 

5291 

5297 

53o3 

53o8 

49 

ii 

3238 

3244 

325o3256 

3262 

326848 

ii 

53i4 

5319 

5325 

533o 

5336 

5342 

48 

12 

3273 

3279 

3285 

329i 

3297 

33o3;47 

12 

5347 

5353 

5358 

5364 

5369 

5375 

47 

i3 

33o9 

33i5 

332i 

3327 

3333 

333946 

i3    538i 

5386 

5392 

5397 

54o3 

54o8 

46 

i4 

3345 

335i 

3357 

3363 

3369 

3375 

45 

i4 

54i4|54i9 

5425 

543o 

5436 

5442 

45 

i5 

338i 

3386 

3392  3398 

34o4 

34io 

44 

i5 

544? 

5453 

5458 

5464 

5469 

5475 

44 

16 

34i6 

3422 

3428  3434 

344o 

3446 

43 

16 

548o 

5486 

549i 

5497 

5502 

55o8 

43 

^7 

3452 

3458 

3464 

3469 

3475 

348  1 

42 

17 

55i4 

55i9 

5525 

553o 

5536 

554i 

42 

18 

348*7 

3493 

3499 

35o5 

35ii 

35i7 

4i 

18 

5547 

5552 

5558 

5563 

5569 

5574 

4i 

19 

3523 

3529 

3535  354o 

3546 

35524o 

'9 

558o 

5585 

559i 

5596 

56o2 

56o7 

4o 

20 

9.983558 

3564 

357o3576 

3582 

3588 

39 

20 

9  9856i3 

56i8 

5624 

5629 

5635 

564o 

39 

21 

3594 

3599 

36o5 

36n 

3617  3623 

38 

21 

5646 

565! 

5657 

5662 

5668 

5673 

38 

22 

3629 

3635364i 

3647 

3653  3658 

37 

22 

5679 

5684 

5690 

5695 

5701 

57o6 

3? 

23 

3664 

367o 

3676I3682 

3688 

3694 

36 

23 

5712 

57i7 

5723 

5728 

5734 

5739 

36 

24 

3700 

37o5 

37n 

37i7 

3723 

3729 

35 

24 

5745 

575o 

5756 

576i 

5767 

5772 

35 

25 

3735 

374i 

3747 

3752 

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3764 

34 

25 

5778 

5783 

5789 

5794 

58oo 

58o5 

34 

26 

377o 

3776 

3782 

3788 

3794 

3799 

33 

26 

58n 

58i6 

5822 

5827 

5832 

5838 

33 

27 

38o5 

38n 

38i7 

3823 

3829 

3835 

32 

27 

5843 

5849 

5854 

586o 

5865 

587i 

32 

28 

384o 

3846 

3852 

3858 

38643870 

3i 

28 

5876 

5882 

5887 

5893 

5898 

59o3 

3i 

29 

3875 

388i 

3887  3893 

38993905 

3o 

29 

59o9 

59i4 

5920 

5925 

593i 

5936 

3o 

3o 
3i 

9.983911 
3946 

39i6 
395i 

3922 
3957 

3928 
3963 

3934  3g4o 
39693975 

29 

28 

3o 
3i 

9.985942 
5974 

5947 
598o 

5952 
5985 

5958 
599i 

5963  5969 
5996  6001 

29 

28 

32 

398i 

3986  3992 

3998 

4oo4!4oio 

27 

32 

6oo7 

6012 

6018 

6023 

6029 

6o34  27 

33 

4oi5 

4O2I 

4027 

4o33 

4o394o45 

26 

33 

6o39 

6o45 

6o5o 

6o56  6061  6067  26 

34 

4o5o 

4o56  4062 

4o68 

4074^4079 

25 

34 

6072 

6o77 

6o83 

6088  6094  6099 

25 

35 

4o85 

4o9i 

4o97  4io3 

4io84ii4 

24 

35 

6io4 

6110 

6n5 

612116126  6i32 

24 

36 

4l20 

4126  4i32  4i37 

4i43!4i49 

23 

36 

6137 

6142 

6i48 

6i53j6i596i64 

23 

37 

38 

4x55 

4190 

4i6i 
4i95 

4i66 
4201 

4172 
4207 

41784184 
42134218 

22 
21 

37 
38 

6169 
6202 

6i75 

6207 

6180 
6212 

6186 
6218 

619116196 
6223  6229 

22 
21 

39 

4224 

423o  4236  4242 

42474253 

2O 

39 

6234 

6239 

6245 

625o 

6256 

6261 

20 

4o 

9.984259 

4265 

427O|4276 

4282  4288 

19 

4o 

9.986266 

6272 

6277 

6282 

6288 

6293 

'9 

4i 

4294 

4299 

43o543ii 

43174322 

18 

4i 

6299 

63o4  63p9 

63i5 

6320 

6325 

18 

42 

4328 

4334434o4345 

435i  4357 

17 

42 

633  1 

6336  6342 

6347 

6352 

6358 

ll 

43 

4363 

43684374438o 

4386,4391 

16 

43 

6363 

6368  6374 

6379 

6384 

6390 

it 

44 

4397 

44o3  4409 

44i4 

4420  4426 

i5 

44 

6395 

64oi 

64o6 

64xi 

6417  6422 

i5 

45 

4432 

44374443 

4449 

4455  446o 

x4 

45 

6427 

6433  6438 

6443 

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i4 

46 

4466 

4472  4477 

4483 

4-4-^Q  4*40^ 

i3 

46 

6459 

6465  647o 

6475 

648  1 

6486 

i3 

47 

45oo 

45o6 

45i245i8 

45234529 

12 

47 

6491 

6497  65o2 

6507 

65i3 

65i8 

12 

48 

4535 

454o  454614552 

45584563 

II 

48 

6523 

6029 

6534 

6539 

6545  655o 

II 

49 

4569 

4575458o4586 

4592  4598 

IO 

49 

6555 

656i 

6566 

6571 

6577!6582 

10 

5o 

9.984603 

4609 

46i5462o 

462614632 

9 

5o 

9.986587 

6593 

6598 

66o3 

66086614 

9 

5i 

4638 

4643  4649  4655 

466c  4666 

8 

5i 

6619 

6624 

663o 

6635 

664o  6646 

8 

52 

4672 

46774683 

4689 

46944700 

7 

52 

665i 

6656666i 

6667 

6672  6677 

7 

53 

47o6 

4712:4717 

4723 

4729  4?34 

6 

53 

6683  6688  6693 

6699 

6704  6709 

6 

54 

474o 

4746 

475i 

4757 

47634768 

5 

54 

6714  6720  6725 

673o 

6736674i 

5 

55 
56 

4774 
48o8 

47804785 
48i448i9 

4791 

4825 

4797  4802 
483i  4836 

4 
3 

55 
56 

6746 
6778 

675i  6757  6762  6767j6773 
6783  6788  6794  6799J68o4 

4 
3 

57 

4842 

4848 

4853 

4859 

48654870 

2 

57 

6809 

68i5  6820  6825 

683i  6836 

2 

58 

'4876 

4882!4887 

4893 

48994904 

I 

58 

684i 

6846  6852  6857  686a]686y 

I 

5o 

49104916,4921 

492749324938 

o 

59 

6873 

68786883 

6888 

6894 

6899 

0 

60"     50"  I 
II 

40" 

30"  |  20"  j  10" 

d 

60" 

50"   40" 

30" 

20" 

10" 

jft 

Co-sine  of  15 

Degrees. 

§ 

Co-sine  of  14  Degrees. 

9 

(  1"  2"  *V  4" 

*P  T*-«J  *  j           " 

5"  6"  7"  8"  9" 

t  <  1"  2"  3"  4"  5"  6"  7"  8"  9" 

*l{  1   1   8 

2 

33455 

in\  1   1   2   2   3  3   4   4   5 

LOGARITHMIC    TANGENTS. 


99 


d 

Tangent  of  74  Degrees. 

_g 

Tangent  of  75  Degrees. 

s 

0" 

10" 

20 

30" 

40" 

50" 

9 

0" 

10" 

20" 

30" 

40" 

50" 

o 

io.5425o4 

2583 

2663 

2742 

2822 

29OI 

59 

0 

io.57i948 

2032 

2116 

22OO 

2285 

2369 

59 

I 

2981 

3o6o 

3i4o 

32I9 

3299 

3378 

58 

I 

2453 

2537 

2622 

27o6 

2790 

2875 

58 

2 

3458 

3538 

36i7 

3697 

3777 

3856 

57 

2 

2959 

3o44 

3i28 

3212 

3297 

338i 

57 

3 

3936 

4oi6 

4095 

4i75 

4255 

4335 

56 

3 

3466 

355o 

3635 

37i9 

38o4 

3888 

56 

4 

44i4 

4494 

4574 

4654 

4733 

48i3 

55 

4 

3973 

4o58 

4i42 

4227 

43n 

4396 

55 

5 

4893 

4973 

5o53 

5i33 

52i3 

5292 

54 

5 

448  1 

4565 

465o 

4735 

48i9 

49o4 

54 

6 

5372 

5452 

5532 

56i2 

5692 

5772 

53 

6 

4989 

5o73 

5i58 

5243 

5328 

54i3 

53 

7 

5852 

5932 

6012 

6092 

6172 

6252 

52 

7 

5497 

5582 

5667 

5752 

5837 

5922 

52 

8 

6332 

6412 

6492 

6572 

6653 

6733 

5i 

8 

6007 

6091 

6i76 

6261 

6346 

6/i3i 

5i 

9 

68i3 

6893 

6973 

7o53 

7i33 

7214 

5o 

9 

65i6 

6601 

6686 

677i 

6856 

694i 

5o 

10 

10.547294 

7374 

7454 

7535 

76i5 

7695 

49 

10 

10.577026 

7II2 

7197 

7282 

7367 

7452 

49 

n 

7775 

7856 

7936 

8016 

8097 

8177 

48 

ii 

7537 

7622 

77o8 

7793 

7878 

7963 

48 

12 

8257 

8338 

84i8 

8498 

8579 

8659 

47 

12 

8o48 

8i34 

82I9 

83o4 

839o 

8475 

47 

i3 

8y4o 

8820 

89oi 

8981 

9062 

9142 

46 

i3 

856o 

8646 

873i 

8816 

8902 

8987 

46 

i4 

9223 

93o3 

9384 

9464 

9545 

9625 

45 

i4 

9073 

9i58 

9243 

9329 

94i4 

gSoo 

45 

i5 

9706 

9787 

9867 

9948 

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.  109 

44 

ii 

9585 

967i 

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44 

16 

10.550190 

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16 

10.580099 

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0997 

1078 

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08-70 

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io4i 

42 

18 

n59 

1240 

1320 

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1482 

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4i 

18 

1127 

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1  384 

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4i 

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1  644 

1725 

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1968 

2049 

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1642 

1728 

1814 

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2072 

4o 

20 

io.552i3o 

2211 

2292 

2373 

2454 

2535 

39 

20 

io.582i58 

2243 

2329 

24i5 

25oi 

2587 

39 

21 

2616 

2697 

2778 

2859 

2940 

3021 

38 

21 

2674 

2760 

2846 

2932 

3oi8 

3io4 

38 

22 

3l02 

3i83 

3265 

3346 

3427 

35o8 

37 

22 

3190 

3276 

3362 

3449 

3535 

362i 

37 

23 

3589 

3670 

3752 

3833 

3914 

3995 

36 

23 

37o7 

3793 

388o 

3966 

4o52 

4i38 

36 

24 

4077 

4i58 

4239 

4321 

4402 

4483 

35 

24 

4225 

43n 

4397 

4484 

457o 

4657 

35 

25 

4565 

4646 

4728 

48o9 

489o 

4972 

34 

25 

4743 

4829 

49i6 

5OO2 

5o89 

5i75 

34 

26 

5o53 

5i35 

52i6 

5298 

5379 

5461 

33 

26 

5262 

5348 

5435 

552i 

56o8 

5694 

33 

27 

5542 

5624 

0705 

5787 

5868 

595o 

32 

27 

578i 

5868 

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6l27 

6214 

32 

28 

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6n3 

6i95 

6276 

6358 

644o 

3i 

28 

63oi 

6387 

6474 

656i 

6648 

6734 

3i 

29 

652i 

66o3 

6685 

6766 

6848 

6930 

3o 

29 

6821 

69o8 

6995 

7o8i 

7i68 

7255 

3o 

3o 

10.557012 

7°93 

7i75 

7257 

7339 

7421 

29 

3o 

10.587342 

7429 

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76o3 

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7776 

29 

3i 

7603 

7584 

7666 

7748 

783o 

7912 

28 

3i 

7863 

795o 

8o37 

8124 

8211 

8298 

28 

32 

7994 

8076 

8i58 

8240 

8322 

84o4 

27 

32 

8385 

8472 

8559 

8647 

8734 

8821 

27 

33 

8486 

8568 

865o 

8732 

88i4 

8896 

26 

33 

8908 

8995 

9o82 

9i69 

9a57 

9344 

26 

34 

8978 

9060 

9142 

9224 

9306 

9388 

25 

34 

943  1 

95i8 

96o5 

9693 

978o 

9867 

25 

35 

9471 

9553 

9635 

9717 

9799 

9881 

24 

35 

9955 

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24 

36 

99^4 

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23 

36 

io.59o479 

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o654 

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0829 

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23 

37 

10.  560467 

o54o 

0622 

0704 

0787 

0869 

22 

37 

ioo4 

io9i 

n79 

1266 

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i44i 

22! 

38 

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1  116 

1199 

1281 

1  364 

21 

38 

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1616 

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21  . 

39 

1  446 

1529 

1611 

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20 

39 

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2230 

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2493 

20 

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10.561941 

2024 

2106 

2189 

2272 

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io.59258i 

2669 

2757 

2845 

2932 

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4i 

2437 

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2602 

2685 

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18 

4i 

3io8 

3i96 

3284 

3372 

346o 

3548 

18 

42 

2933 

3oi6 

3099 

3i8i 

32643347 

ll 

42 

3636 

3724 

38i2 

39oo 

3988 

4076 

17 

43 

343o 

35i2 

3595 

3678 

3761  3844 

16 

43 

4i64 

4252 

434o 

4428 

45i6 

46o4 

16 

44 
45 

3927 

4424 

4oio 
4507 

4o93 
459o 

4i75 
4673 

4258434i 
47564839 

i5 
i4 

44 
45 

4692 

5222 

478i 
53io 

4869 
5398 

4957 
5486 

5o45 
5575 

5i33 
5663 

i5 
i4 

46 

4922 

5oo5 

5o88 

5l72 

5255  5338 

i3 

46 

575i 

584o 

5928 

6oi7 

6io5 

6i93 

i3 

47 

542i 

55o4 

5587 

567o 

57545837 

12 

47 

6282 

637o 

6459 

6547 

6636 

6724 

12 

48 

5920 

6oo3 

6086 

6i7o 

6253^6336 

II 

48 

68i3 

69oi 

699o 

7o78 

7167 

7256 

II 

49 

6420 

65o3 

6586 

6669 

6753:6836 

IO 

49 

7344 

7433 

7522 

76io 

7699 

7788 

10 

5o 

10.566920 

7003 

-7086 

7i7o 

7253  7337 

9 

5o 

io.597876 

7965 

8o54 

8i43 

823i 

8320 

9 

5i 

7420 

75o4 

7587 

767i 

7754'7838 

8 

5i 

84o9 

8498 

8587 

8675 

8764 

8853 

8 

52 

7921 

8oo5 

8088 

8l72 

8255'8339 

7 

52 

8942 

9o3i 

9I20 

92O9 

9298 

9387 

7 

53 

8423 

85o6 

859o 

8674 

8757;884i 

6 

53 

9476 

9565 

9654 

9743 

9832 

992I 

6 

54 

8925 

9008 

9O92 

9176 

92609343 

5 

54 

10.600010 

OIOO 

oi89 

0278 

o367 

o456 

5 

55 

9427 

95  1  1 

9595 

9679 

9763  9846 

4 

55 

o545 

o635 

0724 

o8i3 

0902 

O992 

4 

56 

993o 

..i4 

..98 

.182 

.266  .35o 

3 

56 

1081 

II7O 

1260 

1  349 

i438 

i528 

3 

57 

10.570434 

o5i8 

0602 

0686 

o77o  o854 

2 

57 

161-7 

I7o6 

i796 

i885 

i975  2064 

2 

58 

o938 

IO22 

1106 

1  190 

i274  i358 

I 

58 

2i54 

2243 

2333 

2422 

25l2  26OI 

I 

59 

i442 

l527 

161  1 

:695 

i779  i863 

0 

59 

2691  278i 

287O 

296o 

3o5o3i39 

0 

60" 

50"   40" 

30" 

20"   10" 

. 

60"      50" 

40" 

30" 

20"   10" 

. 

To-tangei-t  of  15  Degrees. 

'% 

Co-tangent  of  14  Degrees. 

§ 

PPartJ  l"  2//  3"  4"  5"  6"  7//  8"  9// 

C  1"  2"  3"  4"  5"  6"  7"  8"  9" 

inl  8  16  25  33  41  49  57  65  74 

irtj  9  17  26  35  43  52  61  69  78 

100 


LOGARITHMIC    SINES. 


1 

Sine  of  76  Degrees. 

_c 

Sine  of  77  Degrees. 

8 

0" 

10" 

20" 

30" 

40" 

50" 

^ 

0"    [  10" 

20" 

30" 

40" 

50" 

o 

9.986904 

6909 

69i5 

6920 

6925 

6930  59 

o 

9.988724|8729 

8734 

8739 

8743 

8748 

59 

i 

6936 

694i 

6946 

6951 

6957 

6962 

58 

I 

8753 

8758 

8763 

8768 

8772 

8777 

58 

2 

6967 

6972 

6978 

6983 

6988 

6993 

57 

2 

8782 

8787 

8792 

8797 

8802 

8806 

57 

3 

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7oo9 

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7019 

7025 

56 

3 

8811 

8816 

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883i 

8835 

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4 

7o3o 

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4 

884o 

8845 

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8855 

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5 

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5 

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45 

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45 

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43 

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9i679i7i 
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91-76 
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43 

17 
18 

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7485  -7490 

42 

4i 

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32 

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42 
43 
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8218 
8247 

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i5 

42 

43 

44 

99i5 

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9919,9924 
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9974  9979 

9929 
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9933 
9961 
9988 

9938 
9965 
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16 
i5 

45    8282 

8287 

8292  8297  83o2 

83o7 

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45 

9997 

.  .  .2 

...6 

.  .  ii 

..16 

.  .20 

i4 

46 

83i2 

83i7 

8322'8327:8332 

8337 

i3 

46 

9.99OO25 

0029 

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4?    8342 

8346 

835i8356836i 

8366 

12 

47 

0052 

0057 

0061 

0066 

00-70 

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12 

48    837i 

8376 

838i'8386839i 

8396 

II 

48 

oo79 

oo84 

0088 

oo93 

0098 

0102 

II 

49    84oi 

84o6 

84n  84168420 

8425 

10 

49 

0107 

01  II 

0116 

OI2O 

OI25 

OI29 

10 

509.988430 

8435 

844o  8445  845o 

8455 

9 

5o 

9.990134 

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9 

5i|    846o 

8465 

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8475  848o 

8484 

8 

5i 

0161 

0166 

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oi75 

01-79 

oi84 

8 

52 

8489 

8494 

8499 

85o4  85o9 

85i4 

7 

52 

0188 

0193 

019-7 

0202 

0206 

02  1  1 

7 

53    85i9 

8524 

8529 

85348538 

8543 

6 

53 

02l5 

0220 

O225 

O229 

0234 

0238 

6 

54    8548 

8553 

8558 

85638568 

8573 

5 

54 

0243 

0247 

O252 

0256 

0261 

0265 

5 

55    8578 

8583 

8587 

8592  8597 

8602 

4 

55 

0270 

0274 

0279 

0283 

0288 

O292 

4 

56 

86o7 

8612 

8617 

86228626 

863i 

3 

56 

0297 

o3oi 

o3o6 

o3io  o3i5 

o3i9 

3 

57 

8636 

864i 

8646 

865i  8656 

8661 

2 

57 

0324 

o328 

o333 

o337o342 

o346 

2 

58    8666 

867o 

8675 

8680  8685 

8690 

I 

58 

o35i 

o355 

o36o 

o364  o369 

o373 

I 

59    8695 

87oo 

8704 

8709  8714 

8719 

0 

59 

o378 

o382Jo386 

o39i  o395 

o4oo 

0 

60" 

50" 

40" 

30"   20" 

10" 

d 

60" 

50"   40" 

30"   20" 

10" 

d 

Co-sine  of  13  Degrees. 

3 

Co-sine  of  12  Degrees. 

i 

.<  1"  2"  3"  4"  5"  6"  7"  8"  9" 

.(  1"  2"  3"  4"  5"  6"  7"  8"  9" 

in\  1   1  2  2   3   3   4   4   5 

""M  01   122   3344 

LiOGARITHMIC     TANGENTS. 


10! 


1 

Tangent  of  76  Degrees. 

d 

Tangent  of  77  Degrees. 

* 

0" 

10" 

20" 

30" 

40" 

50" 

J 

0" 

10" 

20" 

30" 

40" 

50" 

0 

10.603229 

33i9 

34o8 

3498 

3588 

3678 

59 

0 

10.636636 

6732 

6828 

6924 

7020 

7116 

59 

I 

3767 

3857 

3947 

4087 

4127 

4217 

58 

I 

72l3 

73o9 

74o5 

75oi 

7597 

760.4 

58 

2 

43o6 

4396 

4486 

4576 

4666 

47^6 

57 

2 

779° 

7886 

7983 

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8i75 

8272 

57 

3 

4846 

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5026 

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5206 

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56 

3 

8368 

8465 

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8657 

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56 

4 

5386 

5477 

5567 

5657 

5747 

5837 

55 

4 

8947 

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9237 

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55 

5 

5927 

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54 

5 

9526 

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.  .  10 

54 

6 

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6920 

53 

6 

10.640107 

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53 

7 

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7101 

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52 

7 

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1172 

52 

8 

7553 

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7734 

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5i 

8 

I269 

i366 

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17^4 

5i 

9 

8097 

8187 

8278 

8368 

8459 

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5o 

9 

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i948 

2046 

2i43 

2240 

2337 

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10 

10  6o86,4o 

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8822 

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4Q 

10 

io.642434 

253i 

2629 

2726 

2823 

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49 

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12 

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47 

12 

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37oo 

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46 

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4i87 

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4578 

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46 

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0913 

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1186 

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45 

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487i 

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1642 

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16 

1916 

2008 

2099 

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2373 

43 

16 

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6i43 

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6339 

6437 

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2464 

2556 

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2739 

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2922 

42 

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6535 

6633 

673i 

6829 

6927 

7026 

42 

18 

3oi3 

3io5 

3i96 

3288 

3379 

3471 

4i 

18 

7124 

7222 

7320 

74i8 

75i7 

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4i 

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3562 

3654 

3746 

3837 

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4o 

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8008 

8106 

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20 

io.6i4ii2 

4204 

4296 

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4479 

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39 

20 

io.6483o3 

8402 

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8599 

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39 

21 

4663 

4755 

4847 

4938 

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38 

21 

8894 

8993 

9o9i 

9i9o 

9288 

9387 

38 

22 

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37 

22 

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37 

23 

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36 

23 

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36 

24 

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65o3 

6595 

6687 

6779 

35 

24 

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0770 

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o968 

1067 

1166 

35 

25 

6871 

6964 

7o56 

7i48 

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7333 

34 

25 

1265 

1  364 

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1661 

1760 

34 

26 

7425 

75i8 

7610 

7702 

7795 

7887 

33 

26 

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i958 

2o58 

2l57 

2256 

2355 

33 

27 

7980 

8072 

8i64 

8257 

8349 

8442 

32 

27 

4455 

2554 

2653 

2752 

2852 

295l 

32 

28 

8534 

8627 

8720 

8812 

89o5 

8997 

3i 

28 

3o5i 

3i5o 

3249 

3349 

3448 

3548 

3i 

29 

9090 

9183 

9275 

9368 

946i 

9554 

3o 

29 

3647 

3747 

3846 

3946 

4o46 

4i45 

3o 

3o 

10.619646 

9739 

9832 

9925 

..17 

.  no 

29 

3o 

10.654245 

4344 

4444 

4544 

4643 

4743 

29 

3i 

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28 

3i 

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28 

32 

0761 

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1226 

27 

32 

5442 

5542 

5642 

5742 

5842 

5942 

27 

33 

1319 

1412 

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i598 

i69i 

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26 

33 

6042 

6142 

6242 

6342 

6442 

6542 

26 

34 

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1971 

2064 

2167 

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2344 

25 

34 

6642 

6742 

6842 

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7i43 

25 

35 

2437 

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2624 

2717 

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24 

35 

7243 

7344 

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24 

36 

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3090 

3i84 

3277 

3371 

3464 

23 

36 

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7946 

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8i47 

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8348 

23 

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3558 

365i 

3745 

3838 

3932 

4o25 

22 

37 

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8549 

8649 

875o 

885o 

895i 

22 

38 

4119 

42l3 

43o6 

44oo 

4494 

4587 

21 

38 

9o52 

9l52 

9253 

9354 

9454 

9555 

21 

39 

468i 

4775 

4869 

4962 

5o56 

5i5o 

20 

39 

9656 

9757 

9857 

9958 

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.160 

2O 

4o 

10.625244 

5338 

543i 

5525 

56i9 

57I3 

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10.660261 

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0766 

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4i 

5807 

5901 

5995 

6o89 

6i83 

6277 

18 

4i 

0867 

o968 

io69 

II70 

1271 

1372 

18 

42 

6371 

6465 

6559 

6653 

6747 

684i 

?7 

42 

i4?3 

i574 

i676 

i777 

1878 

I979 

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43 

6936 

7o3o 

7124 

7218 

7312 

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16 

43 

2081 

2182 

22-83 

2385 

2486 

2587 

16 

44 

75oi 

7595 

7689 

7784 

7878 

7972 

i5 

44 

2680. 

279° 

2892 

2993 

3o95 

3i96 

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45 

8067 

8161 

8256 

835o 

8444 

8539 

i4 

45 

3298 

3399 

35oi 

36o2 

37o4 

38o6 

i4 

46 

8633 

8728 

8822 

89i7 

9OII 

9io6 

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46 

39O7 

4oo9 

4m 

4212 

43i4 

44i6 

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4? 

9201 

9295 

939o 

9484 

9579 

9674 

12 

47 

45i8 

4620 

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4823 

4925 

5027 

12 

48 

9768 

9863 

9958 

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•  i47 

.242 

II 

48 

5i29 

523i 

5333 

5435 

5537 

5639 

II 

49 

io.63o337 

0432 

0527 

0622 

0716 

0811 

10 

49 

574i 

5843 

5945 

6o47 

6i49 

6252 

IO 

5o 

10.630906 

1001 

io96 

n9i 

1286 

i38i 

9 

5o 

10.666354 

6456 

6558 

6660 

6763 

6865 

9 

5i 

1476 

1571 

1666 

1761 

1867 

I952 

8 

5! 

6067 

7o7o 

7I72 

7274 

7377 

7479 

8 

52 

2047 

2l42 

2237 

2332 

2428 

2523 

7 

52 

7582 

7684 

7787 

7889 

7992 

8o94 

7 

53 

2618 

27l3 

28o9 

29O4 

2999 

3o95 

6 

53 

8i97 

8299 

8402 

85o5 

8607 

8710 

6 

54 

3190 

3285 

338i 

3476 

3572 

3667 

5 

54 

88i3 

89i6 

9oi8 

9I2I 

9224 

9327 

5 

55 

3763 

3858 

3954 

4o49 

4i45 

4240 

4 

55 

943o 

9532 

96359738 

984i 

9944 

4 

56 

4336 

4432 

4527 

4623 

4718 

48i4 

3 

56 

io.67oo47 

oi5o 

0253  o356 

o459 

o562 

3 

5? 

4910 

5oo6 

5ioi 

5i97 

5293 

5389 

2 

57 

0666  o769  o872  o975 

1078 

1181 

2 

58 

5485 

558o 

5676 

5772 

5868 

5954 

I 

58 

1285  i388  i49i  i595 

i698 

1801 

I 

59 

6060 

6i56 

6252 

6348 

6444 

654o 

0 

59 

I9o5  2O08  2112  22l5!23l8  2422 

o 

60" 

50" 

40" 

30" 

20" 

10" 

j 

60"     50"   40"   30"   20"   10"   ^ 

Co-tangent  of  13  Degrees. 

a 

Co-tangent  of  12  Degrees.    ii 

p  p  t5  1"  2"  3"  4"  5"  6"  7"  8"  9" 

.  (  1"  2"  3"  4"  5"  6"  7"  8"  9" 

I  9  19  28  37  46  56  65  74  83 

lrl\  10  20  30  40  50  60  70  80  90 

0-2 


LOGARITHMIC    fc>  i  N  m  B. 


.g 

Sine  of  78  Degrees. 

a      Sine  of  79  Degrees. 

s 

0"     10"  !  20"   30"  i  40" 

50" 

<=•     0"      10" 

20"   30" 

40" 

50" 

0 

9.99o4o4|o4o9  o4i3  o4i8  0422 

0427,59 

09.991947  1951 

1955  1959 

1963 

1967 

59 

I 

2 

o43  1 
o458 

o436  o44o  o445  0449  O454,  58 
0462  0467  0471  0476  o48o  57 

2 

I97i|i975 

1996  2OOO 

1979  i983 
2004  2008 

1987 

2OI2 

1992 
2016 

58 
57 

3 

o485 

0489  0494  0498  o5o3  0507 

56 

3 

2O20  2024 

2028 

2032 

2036 

2040 

56 

4 

o5i  i  o5i6  o52o  o525  0529 

o534 

55 

4 

2044 

2049 

2o53 

2057 

2061 

2o65 

55 

5 

o538  o543  o547  o552  o556jo56o 

54 

5 

2069 

2073 

2077 

2081 

2o85 

2o89 

54 

6 

o565 

05690574  0578  o583 

o587 

53 

6 

2093  2O97 

2101 

2105 

2109 

2ii3  53 

7 

0591 

0596  0600  o6o5  0609  0614 

52 

7 

8Xl8 

2122 

2-126 

2i3o 

2i34 

2i38 

52 

8 

0618 

0622  0627  o63i  o636  o64o 

5i 

8 

2  1  42 

2146 

2I5o 

2i54 

2i58 

2162 

5i 

9 

o645 

0649  o653  o658  0662 

0667 

5o 

9 

2l66 

2170 

2I74 

2178 

2182 

2186 

5o 

IO 

9.990671 

0675  o68olo684o689 

0693 

49 

10 

9.992190 

2194 

2198 

2202 

2206 

2210 

49 

ii 

0697 

0702  0706  o7i  ro7i5 

071948 

i: 

88X4 

22l8 

2222 

2226 

2230 

2234 

48 

12 

0724 

0728073307370741 

0746 

47 

12 

2239 

2243 

2247 

225l 

2255 

2259 

47 

i3 

0750 

0755  0759^7630768 

0772 

46 

i3 

2263 

2267 

2271 

2275 

2279 

2283 

46 

i4 

0777 

0781  0785  0790  0794 

0798 

45 

i4 

2287 

2291 

2295 

2299 

23o3 

2307 

45 

i5 

o8o3 

08070812  08160820 

0825 

44 

i5 

23ll 

23i5 

2319 

2323 

2327 

233i 

44 

16 

0829 

o833  o838  0842 

o847 

o85i 

43 

16 

2335 

2339 

2343 

2347 

235i 

2355 

43 

17 

o855 

08600864  0868 

08  7  3 

o8"77 

42 

17 

2359 

2363 

2366 

2370 

2374 

2378 

42 

18 

0882 

088608900895 

0899 

0903 

4i 

18 

2382 

2386 

2390 

2394 

2398 

2402 

4i 

19 

0908 

0912  0916  0921 

0926 

0929 

4o 

19 

2406 

2410 

24i4 

2418 

2422 

2426 

4o 

20 

9.990934 

0938  0942  0947 

o95i 

0955 

39 

20 

9.992430 

^434 

2438 

2442 

2446 

245o 

39 

21 

0960 

0964  0969  0973 

°977 

0982 

38 

21 

2454 

2458 

2462 

2466 

2470 

2474 

38 

22 

0986 

09900995 

0999 

ioo3 

1008 

37 

22 

2478 

2482 

2485 

2489 

2493 

2497 

37 

23 

1012 

1016  1021 

IO25 

1029 

io33 

36 

23 

25oi 

25o5 

2509 

25i3 

2517 

252i  36 

24 

io38 

1042  io46 

io5i 

io55 

io5g 

35 

24 

2525 

2529 

2533 

2537 

254i 

2545 

35 

25 

1064 

1068  1072 

1077 

1081 

io85 

34 

25 

2549 

2553 

2556 

256o 

2564 

2568 

34 

26 

1090 

1094  1098 

no3 

1  107 

III! 

33 

26 

2572 

2576 

258o 

2584 

2588 

2592 

33 

27 

iiiS 

I  120  I  124 

1128 

n33 

n37 

32 

27 

2596 

2600 

2604 

2607 

261  1 

26i5 

32 

28 

ii4i 

n46  i  i5o 

n54 

n58 

n63 

3i 

28 

2619 

2623 

2627 

263i 

2635 

2639 

3i 

29 

1167 

1171  1176 

1180 

1184 

1x88 

3o 

29 

2643  2647  265  1 

2654 

2658 

2662 

3o 

3o 

9.991193 

I  197  1201 

1206 

1210 

18X4 

29 

3o 

9.992666  2670)2674 

2678 

2682 

2686 

20 

3i 

1218 

1223  1227 

I23l 

1235 

1240 

28 

3i 

2690 

2693  2697 

2701 

2705 

2709 

28 

32 

1244 

1248  1253 

1257 

1261 

1265 

27 

32 

2?l3 

2717 

2721 

2725 

2728 

2732 

27 

33 

1270 

1274  1278 

1282 

1287 

1291 

26 

33 

2736 

274^ 

2744 

2748 

2752 

2756 

26 

34 

1295 

1299  i3o4 

i3o8 

i3I2 

i3i6 

25 

34 

2759 

2763 

2767 

277I 

2775 

2779 

25 

35 

1321 

i325  1329 

i333 

i338 

1  342 

24 

35 

2783 

2787 

2790 

2794 

2798 

2802 

24 

36 

1  346 

i35oi355 

i359 

i363 

i367 

23 

36 

2806 

2810 

2814 

28l8 

2821 

2825 

23 

37    i372 

1376  i38o 

1  384 

i389 

i393 

22 

37 

2829 

2833 

2837 

2841 

2845 

2848 

22 

38    i397 

i4oi  i4o6 

i4io 

i4i4 

i4i8 

21 

38 

2852 

2*56 

2860 

2864 

2868 

2871 

21 

39 

1422 

1427  i43i 

i435 

i439 

1  444 

2O 

39 

2875 

2879 

2883 

2887 

2891 

2895 

20 

4o 

9.991448 

1452  i456 

i46o 

i465 

1469 

19 

4o 

9.992898 

2902 

2906 

2910 

2914 

2918 

I9 

4i 

i4?3 

1477  1482 

i486 

1490 

1494 

18 

4i 

2921 

2925 

2929 

2933 

2937 

2941 

18 

42 

1498 

i5o3  1507 

i5n 

i5i5 

iSig 

'7 

42 

2944 

8948 

29* 

2956 

2960 

2963 

i7 

43 

i524 

i528  i532 

i536 

i54o 

1  545 

16 

43 

2967 

2971 

2975 

2979 

2983 

2986 

16 

44 

1  549 

i553  i557 

i56i 

i566 

i57o 

i5 

44 

2990 

2994 

2998 

3002 

3oo5 

Soog 

i5 

45 

i574 

i578i582 

i586 

1591 

i5g5 

i4 

45 

3oi3 

3017 

3O2I 

3o24 

3028 

3o32 

i4 

46 

i599 

i6o3  1607 

1612 

1616 

1620 

i3 

46 

3o36 

3o4o 

3o43 

3o47 

3o5i 

3o55 

i3 

47 

1624 

1628  i632 

i637 

i64i 

1  645 

12 

47 

SoSg 

3o62 

3o66 

3070 

3o74 

3o78 

12 

48 

i649 

i653i657 

1662 

1666 

i67o 

II 

48 

3o8i 

3o85 

3089 

3o93 

3o97 

3ioo 

II 

49 

1674 

1678  1682 

1687 

1691 

i695 

IO 

49 

3io4 

3io8 

3lI2 

3n5 

3119 

3i23 

IO 

5o 

9.991699 

1703  1707 

1712 

1716 

I720 

9 

5o 

9.993127 

3i3i 

3i34 

3i38 

3i42 

3i46 

9 

5i 

1724 

1728  1732 

1736 

1741 

i745 

8 

5i 

3i49 

3i53 

3i57 

3i6i 

3i65 

3i68 

8 

52 

1749 

1753x757 

1761 

i765 

I77o 

7 

52 

3172 

3i76 

3i8o 

3i83 

3i87 

3191 

7 

53 

1774 

1778  1782 

1786  i79o 

i7g4 

6 

53 

SigSjSigS 

3202 

3206 

3210 

32i3 

6 

54 

1799 

1803.1807 

1811  1816 

1819 

5. 

54 

3217  3221  3225  3228 

3232 

3236 

5 

55 

i823 

1827  i832 

i836  i84o 

1  844 

4 

55    324o3s>43  3247  325i 

32553258 

4 

56 

1  848 

i85ax856 

1860  i865 

1869 

3 

56 

3262:3266  3270  3273  3277'328i 

3 

57 

i873 

18771881 

i885 

1889 

i893 

2 

57 

3284  3288  3292  3296^299  33o3 

2 

58 

1897 

1901  1906 

i9io  i9i4 

1918 

I 

58 

33o733n  33x433x83389  3325 

I 

59 

1922 

1926  1930 

i934  1938 

1942 

O 

59 

3329  3333  3337334o'3344  3348  o 

60"     50"  |^40"   30"  j  20" 

10" 

A 

60"     50"   40"   30"  ;  SO"   10"  .  „• 

Co-sine  of  1  1  Degrees. 

§ 

Co-sine  of  10  Degrees.     ?* 

P  Part*  l"  2"  3"  4//  5"  6"  7// 

8"  9"  |      .(1"  2"  3"  4"  5"  6"  7"  8"  9" 

iTli  0   1   1   2   2   3   3 

34       '"}  0   11222334 

LOGARITHMIC    TANGENTS. 


103 


1 

Tangent  of  78  Degrees. 

.5 

Tangent  of  79  Degrees. 

g 

0" 

10" 

20" 

30" 

40" 

50" 

% 

0" 

10" 

20" 

30" 

40" 

50" 

o 

10.672525 

2629 

2733 

2836 

2940 

3o43 

59 

o 

10.711348 

i46o 

i573 

i685 

I798 

1910 

59 

I 

3i4? 

325i 

3354 

3458 

3562 

3666 

58 

i 

2023 

2i35 

2248 

236i 

2473 

2586 

58 

2 

3769 

3873 

3977 

4o8i 

4i85 

4289 

57 

2 

2699 

2811 

2924 

3o37 

3i5o 

3263 

57 

3 

4393 

4497 

46oi 

47o5 

48o9 

49:3 

56 

3 

3376 

3488 

36oi 

37i4 

3827 

3940 

56 

4 

5017 

5l2I 

5225 

5329 

5433 

5537 

55 

4 

4o53 

4i67 

4280 

4393 

45o6 

46i9 

55 

5 

5642 

5746 

585o 

5954 

6059 

6i63 

54 

5 

4732 

4846 

4959 

5072 

5i85 

5299 

54 

6 

6267 

6372 

6476 

658o 

6685 

6789 

53 

6 

54i2 

5526 

5639 

5752 

5866 

5979 

53 

7 

6894 

6998 

7io3 

7207 

73i2 

7417 

52 

7 

6093 

62O7 

6320 

6434 

6547 

6661 

52 

8 

7521 

7626 

773i 

7835 

794o 

8o45 

5i 

8 

6775 

6889 

7002 

7116 

723o 

7344 

5i 

9 

8149 

8254 

8359 

8464 

8569 

8674 

5o 

9 

7458 

7572 

7686 

7799 

79i3 

8027 

5o 

10 

8778 

8883 

8988 

9o93 

9198 

93o3 

49 

10 

8142 

8256 

837o 

8484 

8598 

8712 

49 

ii 

94o8 

95i3 

9618 

9723 

9829 

9934 

48 

1  1 

8826 

894i 

9o55 

9l69 

9283 

9398 

48 

12 

10  680039 

oi44 

0249 

o355 

o46o 

o565 

47 

12 

9512 

962-7 

974i 

9856 

997° 

..85 

47 

i3 

0670 

0776 

0881 

0987 

1092 

ii97 

46 

i3 

10.720199 

o3i4 

0428 

o543 

o658 

0772 

46 

i4 

i3o3  1408 

i5i4 

1619 

1725 

i83o 

45 

i4 

0887 

1  002 

1116 

I23l 

1  346 

i46i 

45 

i5 

1936 

2042 

2147 

2253 

2359 

2464 

44 

1  5 

1576 

1691 

1806 

1921 

2036 

2l5l 

44 

16 

2570 

2676 

2782 

2887 

2993 

3o99 

43 

16 

2266 

238i 

2496 

2611 

2726 

2841 

43 

!? 

32o5 

33n 

34i7 

3523 

3629 

3735 

42 

*7 

2957 

3o72 

3i87 

3302 

34i8 

3533 

42 

18 

384i 

3947 

4o53 

4i59 

4265 

4371 

4i 

18 

3649 

3764 

3879 

3995 

4uo 

4226 

4i 

J9 

4477 

4584 

4690 

4796 

4902 

5oo9 

4o 

*9 

4342 

4457 

4573 

4688 

48o4 

4920 

4o 

20 

5n5 

5221 

5328 

5434 

554o 

5647 

39 

20 

5o36 

5i5i 

5267 

5383 

5499 

56i5 

39 

21 

5753 

586o 

5966 

6073 

6179 

6286 

38 

21 

5731 

5847 

5963 

6o79 

6195 

63ii 

38 

22 

6392 

6499 

6606 

6712 

6819 

6926 

3? 

22 

6427 

6543 

6659 

6775 

6891 

7008 

37 

23 

7032 

7i39 

7246 

7353 

7460 

7567 

36 

23 

7124 

7240 

7356 

7473 

7589 

7706 

36 

24 

7673 

7780 

7887 

7994 

8101 

8208 

35 

24 

•7822 

7938 

8o55 

8i7i 

8288 

84o5 

35 

25 

83i5 

8422 

8529 

8636 

8744 

885i 

34 

25 

852i 

8638 

8754 

887i 

8988 

9io5 

34 

26 

8958 

9o65 

9172 

9280 

9387 

9494 

33 

26 

9221 

9338 

9455 

9572 

9689 

98o6 

33 

27 

9601 

97°9 

9816 

9924 

..3i 

.i38 

32 

27 

9923 

..4o 

.i57 

.274 

.39i 

.5o8 

32 

28 

10.690246 

o353 

o46i 

o568 

0676 

0784 

3i 

28 

io.73o625 

0742 

0860 

°977 

1094 

I2II 

3i 

29 

0891 

°999 

1107 

I2l4 

1322 

i43o 

3o 

29 

1329 

1  446 

i563 

1681 

1-798 

I9i6 

3o 

3o 

i537 

1  645 

i753 

1861 

i969 

2077 

29 

3o 

2o33 

2l5l 

2268 

2386 

25o3 

2621 

29 

3i 

2184 

2292 

2400 

25o8 

2616 

2724 

28 

3i 

2739 

2856 

2974 

3o92 

32IO 

3327 

28 

32 

2832 

294i 

3o49 

3i57 

3265 

3373 

27 

32 

3445 

3563 

368i 

3799 

39i7 

4o35 

27 

33 

3481 

359o 

3698 

38o6 

39i4 

4023 

26 

33 

4i53 

4271 

4389 

45o7 

4625 

4?44 

26 

34 

4i3i 

4239 

4348 

4456 

4565 

4673 

25 

34 

4862 

4980 

5o98 

52i7 

5335 

5453 

25 

35 

4782 

489o 

4999 

5107 

52i6 

5325 

24 

35 

5572 

5690 

58o9 

5927 

6o46 

6:64 

24 

36 

5433 

5542 

565i 

5759 

5868 

5977 

23 

36 

6283 

64oi 

6520 

6639 

6757 

6876 

23 

3? 

6086 

6i95 

63o3 

6412 

652i 

663o 

22 

37 

6995 

7ii3 

7232 

735! 

7470 

7589 

22 

38 

6739 

6848 

6957 

7066 

7175 

7284 

21 

38 

77o8 

7827 

7946 

8o65 

8i84 

83o3 

21 

39 

7393 

75o3 

7612 

7721 

783o 

7939 

20 

39 

.  8422 

854i 

8660 

878o 

8899 

9018 

2O 

4o 

8049 

8i58 

8267 

83?6 

8486 

8595 

I9 

4o 

9i37 

9257 

9376 

9496 

9615 

9734 

'9 

4i 

8705 

88i4 

8924 

9o33 

9i43 

9252 

18 

4i 

9854 

9973 

..93 

.213 

.332 

.452 

18 

42 

9362 

94?i 

958i 

9691 

98oo 

99io 

r7 

42 

io.74o57i 

0691 

0811 

o93i 

io5o 

1170 

17 

43 

10.700020 

OI29 

O239 

o34g 

o459 

o569 

16 

43 

1290 

i4io 

i53o 

i65o 

1770 

1890 

16 

44 

0678 

0788 

o898 

1008 

1118 

1228 

i5 

44 

2OIO 

2i3o 

225o 

2370 

2490 

2611 

i5 

45 

i338 

1  448 

i558 

1668 

1779 

i889 

i4 

45 

273l 

285i 

297I 

3o92 

3212 

3332 

i4 

46 

1999 

2I09 

22I9 

233o 

244o 

255o 

i3 

46 

3453 

3573 

3694 

38i4 

3935 

4o55 

i3 

4? 

2661 

2771 

288l 

2992 

3l02 

32i3 

12 

47 

4176 

4297 

4417 

4538 

4659 

4779 

13 

48 

3323 

3434 

3544 

3655 

3765 

3876 

II 

48 

4900 

5O2I 

5i42 

5263 

5384 

55o5 

II 

49 

3987 

4o97 

4208 

43i9 

4429 

454o 

10 

49 

5626 

5747 

5868 

5989 

6110 

623i 

IO 

5o 

465i 

4762 

4873 

4984 

5o95 

52o5 

9 

5o 

6352 

64?3 

6595' 

67i6 

6837 

6959 

9 

5i 

53i6 

5427 

5538 

5649 

5761 

5872 

8 

5i 

7080 

7201 

7323 

7444 

7566 

7687 

8 

52 

5g83 

6o94 

62o5 

63i6 

6428 

6539 

7 

52 

7809 

793o 

8o52 

8174 

8295 

8417 

7 

53 

665o 

6761 

6873 

6984 

7°95 

7207 

6 

53 

8539 

8661 

8782 

89o4 

9026 

9i48 

6 

54 

73i8 

?43o 

754i 

7653 

7764 

7876 

5 

54 

9270 

9392 

95i4 

9636 

9758 

9880 

5 

55 

7987 

8o99 

8211 

8322 

8434 

8546 

4 

55 

io.75ooo2 

0124 

0247 

o369 

0491 

o6i3 

4 

56 

8658 

8769 

8881 

8993 

9io5 

92I7 

3 

56 

o736 

o858 

o98o 

uo3 

1225 

1  348 

3 

57 

9329 

944i 

9553 

9665 

9777 

9889 

2 

$7 

1470 

i593 

1715 

i838 

1961 

2o83 

2 

58 

10.710001 

on3 

0225 

o337 

0449 

o562 

I 

58 

2206 

2329 

2452 

2574 

2697 

2820 

I 

l(l 

0674 

0786 

o898 

IOII 

1123 

1235 

0 

59 

2943 

3o66 

3i89 

33i2 

3435 

3558 

O 

60" 

50" 

40" 

30" 

20" 

10" 

d 

60" 

50" 

40" 

30" 

20"  |  10" 

. 

Co-tangent  of  1  1  Degrees. 

.3 

s 

Co-tangent  of  10  Degrees. 

3 

p  p*  t$  1"  2//  3"  4"  5"  6//  7"  8''  9" 

.  (  1"  2"  3"  4"  5"  6"  7"  8"  9" 

irt}  11  22  32  43  54  65  75  86  97 

in\  12  23  35  47  59  70  82  94  106 

104 


LOGARITHMIC    SINES. 


1 

Sine  of  80  Degrees. 

a 

Sine  of  6  1  Degrees. 

M 

0" 

10" 

20" 

30" 

40" 

50" 

* 

0"      10"   3)»  '  30" 

50" 

o 

9.993351 

3355 

3359 

3363 

3366 

3370 

59 

0 

9.99462o  4623  4627  463o  4633 

4637 

59 

i 

3374 

3377 

338i 

3385 

3389 

3392 

58 

I 

464o:46434647465o4653 

4657 

58 

2 

3 

3396 
34i8 

34oo 
3422 

34o3 
3426 

34o7 
3429 

34n 
3433 

34i4 
3437 

56 

2 

3 

466o!4663  4667  467o!4673 
468o|4683  4686  46904693 

4676 
4696 

57 
56 

4 

344o 

3444 

3448 

345  1 

3455 

3459 

55 

4 

47oo  47o3  47o6  47io  47i3 

47i6 

55 

5 

3462 

3466 

3470 

3473 

3477 

348i 

54 

5 

4720  4723  4726  4729 

4733 

4736 

54 

6 

3484 

3488 

3492 

3495 

3499 

35o3 

53 

6 

4739  4743  4746  474g  4752 

4756 

53 

7 

35o6 

35io 

35i4 

35i7 

352i 

3525 

52 

7 

4759!4762 

4766 

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4776 

52 

8 

3528 

3532 

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3539 

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5i 

8 

477u  47S- 

4785 

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9 

355o 

3554 

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3565 

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5o 

9 

4798  4802 

48o5 

48o8 

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10 

9.993572 

3576 

358o 

3583 

3587 

359i 

49 

10 

9.9948i8 

4821 

4825 

4828483i 

4834 

4y 

ii 

3594 

3598 

36oi 

36o5 

36o9 

36i2 

48 

ii 

4838 

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4844 

4848485i 

4854 

48 

12 

36i6 

3620 

36233627 

363i 

3634 

47 

12 

4857 

486i 

4864 

4867 

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4874 

47 

i3 

3638 

364i 

3645 

3649 

3652 

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46 

i3    4877 

488o 

4883 

488-714890 

4893 

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i4 

366o 

3663 

3667 

367o 

3674  3678 

45 

i4 

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49i3 

45 

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368i 

3685 

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3699 

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i5 

49-6 

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4922 

4920  4929 

493s 

44 

16 

37o3 

37o7 

37103714 

37i7 

3721 

43 

16 

4935 

4938 

4942 

49454948 

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17 

3725 

3728 

3732 

3735 

3739 

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42 

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4955 

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496i 

4964 

4968 

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4s 

1  8 

3746 

375o 

3753 

3757 

376i 

3764 

4i 

18 

4974 

4977 

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4i 

19 

3768 

377i 

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3779 

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4993 

4997 

5ooo 

5oo3 

5oo6 

5oo9 

4c 

20  9.993789 

3793 

3797 

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38o4 

38o7 

39 

20 

9.995oi3 

5oi6 

5oi9 

5022 

5o25 

5o29 

39 

21 

38n 

38i4 

38i8 

3822 

3825 

3829 

38 

21 

5o32 

5o35 

5o38 

5o4i 

5o45 

5o48 

38 

22 

3832 

3836 

384o 

3843 

3847 

385o 

37 

22 

5o5i 

5o54 

5o57 

5o6i 

5o64 

5o67 

3? 

23 

3854 

3857 

386i 

3864 

3868 

3872 

36 

23 

5o7o 

5o73 

5o77 

5o8o 

5o83 

5o86 

36 

24 

3875 

3879 

3882 

3886 

3889 

3893 

35 

24 

5o89 

5o92 

5o96 

5o99 

5  1  02 

5io5 

35 

25 

3897 

39oo 

39o4 

39o7 

39u 

39i4 

34 

25 

5ioS 

5l  12 

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5  u  8 

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34 

26 

3918 

392i 

3925 

3928 

3932 

3936 

33 

26 

5l27 

5i3i 

5i345i37 

5i43 

33 

27 

3939 

3943 

3946 

3c;5o 

3953 

3957 

32- 

27 

5i46 

5i5o 

5i535i56 

5i59 

5i62 

32 

28 

3960 

3964 

3967 

397i 

3974 

3978 

3i 

28 

5i65 

5i69 

•")  i  -  .j 

5i75 

5i78 

5i8i 

3i 

29 

3982 

3985 

3989  3992 

3996 

3999 

3o 

29 

5i84 

5i88 

5i9i 

5i94 

5i97 

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3o 

3o 

9.994003 

4oo6 

4oio  4oi3 

4oi7 

4020 

29 

3o 

9.9952o3 

52o6 

5ai3 

5ai6 

52I9 

29 

3i 

4024 

4027 

4o3i 

4o34 

4o38 

4o4i 

28 

3i 

5222 

5225 

5228 

5232 

5235 

5238 

28 

32 

4o45 

4o48 

4o52 

4o55 

4o59 

4062 

27 

32 

524i 

5-244 

524  7 

525o5253 

5257 

27 

33 

4o66 

4o69 

4o73  4076 

4o8o 

4o83 

26 

33 

526o 

5263 

5266 

5269|5272 

5275 

26 

34 

4o87 

4o9o 

4094  4097 

4ioi 

4io4 

25 

34 

5278 

5282  5285 

5288|529i 

5294 

25 

35 
36 
37 

4io8 
4129 
4i5o 

4m 

4l32 

4i53 

4i364i39 
4i574i6o 

4l22 

4i43 
4i64 

4i25 
4i46 
4i67 

24 
23 
22 

35 
36 
37 

5297 
53i6 
5334 

53oo 
53i9 
5338 

53o3 

5322 

534i 

53o7 
5325 
5344 

53ro 
5328 
5347 

53i3 
533i 
535o 

24 
23 
22 

38    4i7i 

4174 

4i784i8i 

4i844i88 

2  I 

38 

5353 

5356 

5359 

5362 

5365 

5369 

21 

39    4i9i 

4i95 

4198  4202 

42o5 

4209 

20 

39 

5372 

5375|5378 

538i 

5384 

5387 

20 

4o 
4i 

42 

9.994212 
4233 
4254 

4216 
4236 
4257 

4219  4223 
42404243 
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42264230 
42474250 
42674271 

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18 

17 

4o 
4i 

42 

9.99539o 
54o9 

5427 

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5433 

5399  54<>3 
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5424 
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19 

1  8 

43 

4274 

4278 

4281 

4285 

4a88  4292 

16 

43 

5446 

5449 

5452  5455  5458 

546  1 

16 

44 
45 

4295 
43i6 

4298 
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43o2  43o5 
43224326 

43o9;43i2 
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i5 

:4 

44 
45 

5464  5467 
5482  5485 

547oi5473<5476i5479 
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i5 

i4 

46 

4336 

434o 

4343 

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4353 

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46 

55oi 

55o455o7  55io55i3|55i6 

i3 

47 

4357 

436o 

4363 

4367!437o 

4374 

12 

47 

55i9  5522  5525 

5528553i|5534 

12 

48 

4377 

438i 

4384 

43S7 

439i 

4394 

I  I 

48 

5537 

554o 

5543 

5546  5549  555a 

I  I 

49 

4398 

44oi 

44o4 

44o844n 

44i5 

10 

49 

*555 

5558556i 

55645567:557oio 

5o  9.9g44i8 

4421 

44254428:44324435 

9 

5o 

9.995573  5576  5579 

5582  55855588 

9 

5! 

4438 

4442 

4445 

4448:4452  4455 

8 

5  1 

559i 

5594  5597  56oi  56o4  56o7 

8 

52 

4459 

4462 

4465 

4469  4472  4476 

7 

52 

56io  56i3  56i6  56i9  5622  5625 

7 

53 

4479 

4482 

4486'4489i4492!4496 

6 

53 

56285631,5634 

5637,564o5643 

6 

54 

4499 

45o3 

45o6 

45o9:45i345i6 

5 

54 

5646  5649  5o52 

56555658 

566i 

5 

55 

45i9 

4523 

4526 

453o4533  4536 

4 

55 

56645667567o5672  5675 

5678 

4 

56 

454o 

4543 

4546 

455o 

4553 

4556 

3 

56 

568i  56845687569o5693 

5696 

3 

57 

456o 

4563 

4566 

457o 

4573 

4576 

2 

57 

5699  5702  57o5  57o8  57n 

57i4 

2 

58 

458o 

4583 

4587 

459o 

4593 

4597 

I 

58 

57i7  572o  5723|5726  5729 

5732 

I 

59 

46oo 

46o3 

46o7 

4610  46i3 

46i7 

0 

59 

5735  5733  574i  5744  5747  575o 

0 

60" 

50" 

40" 

30"   20" 

10" 

S3 

60"    .50"   40"   30"   20"   10" 

. 

Co-sine  of  9  Degrees. 

§ 

Co-sine  of  8  Degrees. 

m 

5"  6"  7"  8"  9" 

p  p  A  1"  2"  3"  4"  5"  6"  7"  8"  y  ' 

P.PartJ  Q   l   l   l 

22233 

in\  0   1   1   1   2   2   2   3   3 

LOGARITHMIC    TANGENTS. 


105 


.5 

Tangent  of  80  Degrees. 

d 

Tangent  of  81  Degrees. 

2 

0" 

10" 

20" 

30" 

40"  |  50" 

* 

0"      10"  |  20" 

30"  1  40"  i  50"  j 

o 

10-  a5368i 

38o4 

3928 

4o5i 

4l74l4297 

r 

0 

10.800287 

0424 

o56o 

o696 

08330969)59 

i 

442i 

4544 

4667 

4791 

49i4l5o38 

58 

i 

Ilo6 

1242 

i379 

i5i6 

i652  1789^8 

2 

5i6i 

5285 

5408 

5532 

5655  5779 

57 

2 

I926 

2062 

2199 

2336 

2473  2610  57 

o 

59o3 

6026 

6i5o 

6274 

6398  6522 

56 

3 

2747 

2884 

3021 

3i58 

3295|3433 

56 

4 

6646 

6770 

6894 

7018 

7142  7266 

55 

4 

357o 

37o7 

3844 

3982 

4i  19  4257 

55 

5 

739o 

75i4 

7638 

7762 

78868011 

54 

5 

4394 

45J2 

4669 

48o7 

4944  5o82 

54 

6 

8i35 

8259 

8384 

85o8 

8633  8757 

53 

6 

5220 

5358i5495 

5633 

5771  590953 

7 

8682 

9oo6 

9i3i 

9255 

938o  95o5 

52 

7 

6047 

6i85 

6323 

646  1 

65996738|52 

8 

9629 

9754 

9879 

...4 

.128  .253 

5i 

8 

6876 

7oi4 

7l52 

729i 

7429756851 

9 

io.76o378 

o5o3 

0628 

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0878  ioo3 

5o 

9 

7706 

7845 

7983 

8122 

8261,8399  5o 

10 

ii 

1128 

1880 

1253 
2oo5 

i379 
2i3o 

i5o4 

2256 

238i  2507 

49 

48 

10 

II 

8538 
937i 

8677 
95io 

8816 
9649 

89549o939232 
97889928  ..67 

49 
48 

12 

i3 

2532 

3386 

2758 
35i2 

2883 
3638 

3009 
3763 

3i35!326o 
38894oi5 

47 
46 

12 

1  3 

10.810206 

1042 

o345 
1182 

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l322 

0624 
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0^04.  ooo3 
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47 
46 

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4i4i 

4267 

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45 

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1880 

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244o  258o 

45 

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4897 

6024 

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5276 

5402  5529 

44 

i5 

2720 

2860 

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3i4o 

32803421 

44 

16 

5655 

5781 

59o8 

6o34 

6161  6287 

43 

16 

356i 

3701 

3842 

3982 

4122  4263 

43 

17 

64i4 

654o 

6667 

6794 

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42 

17 

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18 

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7681  7808 

4i 

18 

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20 

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21 

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38 

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38 

22 

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22 

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23 

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36 

24 

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26 

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27 

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4200 

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32 

27 

29i6 

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32o3 

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348^3633 

32 

28 

4844 

4973 

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523i 

536o  5489 

3i 

28 

3776 

3920 

4o63 

4207 

435o!4494 

3i 

29 

56i8 

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5876 

6006 

6i35  6264 

3o 

29 

4638 

4782 

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3o 

3o 

6393 

6523 

6652 

6782 

69n  7041 

29 

3o 

55oi 

5645 

5789 

5933 

6o78  6222 

29 

3i 

7i7o 

73oo 

7429 

7559 

7689  7818 

28 

3i 

6366 

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6655 

6799 

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28 

32 

7948 

8078 

8208 

8338 

8468  8598 

27 

32 

7233 

7377 

7522 

7667 

78i2l7956j27 

33 

8728 

8858 

8988 

9118 

9248  9378 

26 

33 

8101 

8246 

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8536 

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26 

34 

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9639 

9769 

9899 

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25 

34 

8971 

9116 

9261 

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25 

35 

10.  7802(20 

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24 

35 

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24 

36 

1074 

1204 

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23 

36 

10.830716 

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1008 

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i299  i445 

23 

37 

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2  I  2O 

225l 

2382  25i3 

22 

37 

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2029 

2175  2322 

22 

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2644 

2775 

2907 

3o38 

3i69  33oo 

21 

38 

2468 

2614 

2760 

2907 

3o53  3200 

21 

39 

3432 

3563 

3695 

3826 

3957  4o89 

20 

39 

3346 

3493 

3639 

3786 

3933'4o8o 

20 

4o 

4220 

4352 

4484 

46i5 

4747'4879 

T9 

4o 

4226 

4373 

4520 

4667 

48i4  496i 

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4i 

Son 

5i42 

5274 

54o6 

5538  5670 

18 

4i 

5i68 

5255 

54o2 

555o 

5697  5844 

18 

42 

58o2 

5934 

6066 

6i98 

633o6463 

ll 

42 

5992 

6139 

6287 

6434 

6582  6729 

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43 

6595 

6727 

6859 

6992 

7124  7257 

16 

43 

6877 

7025 

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7320 

7468  7616 

16 

44 

7389 

7522 

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7787 

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44 

7764 

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8060 

8208 

8356  85o4 

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45 

8i85 

83i7 

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8583 

8716,8849 

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45 

8653 

8801 

8949 

9098 

92469395 

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46 

8982 

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9543 

9692 

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9989 

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i3 

47 

978o 

99i3 

..46 

.180 

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12 

47 

io.84o435 

o584 

o733 

0882 

io3i  1180 

12 

48 

io.79o58o 

0713 

0847 

o98o 

ii  i4  1247 

I  I 

48 

i329 

i479 

1628 

1777 

i926  2076 

II 

49 

1  38-i 

i5i5 

1  648 

1782 

I9i6  2o5o 

IO 

49 

2225 

2375  2524 

2674 

2823i2973 

10 

5o 

2i83 

2317 

245  1 

2585 

27i9  2853 

9 

5o 

3123 

3372(3422 

3572 

3722  3872 

9 

5i 

2987 

3l22 

3256 

339o 

3524J3658 

8 

5i 

4022 

4l72j4322 

4472 

4623^773 

8 

52 

53 

3793 
46oo 

3927 
4734 

4062 
4869 

4196 
5oo4 

433i  4465 
5i38|5273 

7 

6 

52 

53 

4923 
5826 

5o74  5224  5374 
5977161276278 

5525  5675 
6429658o 

7 
6 

54 

54o8 

5543 

5678 

58i2 

5947  6082 

5 

54 

6731  6882|7o33  7184 

7335  7486 

5 

55 

6218 

6353 

6488 

6623 

67586893 

4 

55 

7637  7789  794o  8o9i 

8243;8394 

4 

56 

784? 

7977 

7299 
8112 

7435 
8248 

7570  7706 
8384  85i9 

3 

2 

56 

8546  8697;8849  9001 
9456  96081976019912 

9i52  93o4 
..64  .216 

3 

2 

58 
59 

8655 
94?i 

879i 
96o7 

8927 
9743 

9o63 
9879 

9199  9335 
.  .  i5  .  i5i 

I 

O 

58 
59 

io.85o368  o52o  0672  0825 
I282;i434  1  587  i739 

0977  II29 
l892  2045 

I 
0 

60" 

50"   40" 

30" 

20"   10" 

rf 

60"    i  50"  j  40"   30"  |  20"  i  10" 

, 

Co-tangent  of  9  Degrees 

i 

Co-tangent  of  8  Degrees.     3 

P  Pa  t5  *"  2"  3//  4"  5"  6"  7"   8//   9' 

J  13  26  39  52  65  78  91  103  116 

.  (  1"  2"  3"  4"  5"  6"  7"  8"  9" 
in)  14  29  43  58  72  86  101  115  130 

00 


LOGARITHMIC    SINES. 


g      Sine  of  82  Degrees. 

a 

Sine  of  83  Degrees. 

I 

0"    1  10"   20" 

30" 

40" 

50"  | 

s 

0"     10"  j  2u        i  ) 

50" 

o 

9.995753 

5756 

5759 

5762 

5765|576859 

O 

9.996751  6753  6756,675*  6761 

6764 

59 

2 

577i 
5788 

5773 
579i 

5776 
5794 

5779 
5797 

5782578558 
58oo58o357 

I 

2 

6766;6769  677i  67746777 
67826784678767896792 

6779 
6795 

58 
5? 

3 

58o6 

58o9 

58i2 

58i5 

58i8 

582i 

56 

3 

6797  6800  6802  68o5  6807 

6810 

56 

4 

5823 

5826 

5829 

5832 

5835 

583855 

4 

68i268i5  6818  682. 

6825 

55 

5 

584i 

5844 

5847 

585o 

5853 

585654 

5 

6828;683o  6833  6835  6838 

684i 

54 

6 

5859 

5862 

5864 

5867 

587o 

587353 

6 

6843  6846  6848:685i 

6853 

6856 

53 

7 

5876 

5879 

5882 

5885 

5888 

589ii52 

7 

6858,686i  .6*63  6866 

6869 

687i 

52 

8 

5894 

5897 

5899 

59O2 

59o5 

59o8 

5i 

8 

6874687r 

6884 

6886 

5i 

9 

59n 

59i4 

59i7 

5920 

5923 

5926 

5o 

9 

6889  689  1  689  . 

6899 

69oi 

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48 

6562 

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48 

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53 

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6 

53 

7520 

7523 

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6 

54 

6657 

6660 

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5 

54    7534  7536 

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7543 

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5 

55 
56 
57 

6673 
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3 

2 

55 
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7559 

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4 
3 

2 

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6720 

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58 

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59 

6735 

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59 

7601  760^  -6o5  7608  7610  7612  o 

60" 

50" 

40" 

30"   ;  20" 

10" 

c 

60"     50"   40"  !  30"   20"  i  10" 

Co-sine  of  7 

Degrees. 

s 

Co-sine  of  6  Degrees.      £ 

(  1"  9"  <*   4' 

1    T»  T»    *  1   *      --       '      * 

£"  6"  7" 

8"  9" 

(  l"  2"  3"  4"  5"  6"  7"  8 

P.PartJ  |  !  i  | 

1  2  2 

2   2 

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LOGARITHMIC    TANGENTS. 


107 


1 

Tangent  of  82  Degrees. 

.= 

Tangent  of  83  Degrees. 

m 

0"     |  10" 

20" 

30" 

40" 

50" 

•" 

0"      10"   20"  |  30"  |  40" 

50" 

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10.852197 

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10.910856 

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1727 

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3n5 

3268 

3421 

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3728 

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58 

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I902 

2076 

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2426 

2600 

2775 

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2 

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4495 

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2 

295o 

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3475 

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3825 

57 

3 

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3 

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4527 

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4 

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7 

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1  347 

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4 

56 
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790718080 

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3 

2 

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3746  3946 
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58 

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7773  7975 

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O 

60" 

50" 

40"|  30"   20" 

10" 

c 

60"      50"   40"   30"   20"   10" 

a 

Co-tangent  of  7  Degrees. 

s 

Co-tangent  of  6  Degrees. 

§ 

.<  1"  2"  3"  4"  5"  6"  7"  8"  9" 
I  16  33  49  65  81  98  114  130  146 

.  C  1"  2"  3"  4"  5"  6"  7"  8"  9" 
in\  19  37  56  75  94  112  131  150  168 

108 


LOGARITHMIC    SINES. 


.5 

Sine  of  84  Degrees. 

.5 

Sine  of  85  Degrees. 

a 

0"    !  10"  |  20"  '  30"  1  40"   50" 

a 

0"      10" 

20" 

30"   40" 

50" 

( 

9.997^14  7617  7619  7621/7623  7626 

59 

o  9.998344:8346 

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59 

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762817630  7632  7634:7636  7639 

58 

8355  8357 

8359 

836il8363 

8364 

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2 

3 

764  J 

764376457647:76507662 
7656  76687661  '76637665 

56 

2 

8366  8368 
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83728374 
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8375 
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56 

4 

7667 

7669  7672  7674:7676  7678 

55 

i 

8388 

8390 

8392 

8394 

8395 

8397 

55 

5 

768o 

7682  7686  7687  7689  7691 

54 

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54 

6 

7693 

7696  7698  7700  7702  7704 

53 

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53 

7 

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77097711  7713:77167717 

62 

7 

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8422 

8424 

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52 

8 

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7722  7724  7726,7728(7730 

61 

8 

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8433  8435 

8437 

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5i 

9 

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5o 

c 

8442 

8444  8446  8448 

8449 

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5o 

10 

9.997745 

7747  7760  7762  7754:7756 

49 

10 

9.998453 

8455:845618458 

846o 

8462 

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ii 

12 

7758 
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7760  7762  7765  7767J7769 
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ii 

8464 
8474 

84668467 
8476  8478 

|8469 

8479 

847i 
848  1 

8472 
8483 

48 
47 

iJ 

7784 

7786  7788  7790  7792  7794 

46 

i' 

8485 

8487 

848* 

849o 

8492 

8494 

46 

i4 
i5 

7797 
78o9 

7799  78oi  78o3  78o5  7807 
7811  7814  78167818  782o 

45 
44 

n 
16 

8496 
85o6 

849-718499 

85o8|85o9 

85oi 
85u 

8602 
85i3 

85o4 
85i5 

45 
44 

16 

7822 

7835 

78247826782878307833 
78377839784il78437845 

43 

42 

16 
17 

85ib 
8527 

85i8|852o 
8629  853o 

8522 

8532 

85-^3 
8534 

8626 
8535 

43 

42 

18 

7847 

7849  7852  7864:7866  7868 

4x 

18 

8537 

8539 

854i 

8542 

8544 

8546 

4i 

19 

786o 

7862  7864  7866  7868  7870 

4o 

19 

8548 

8549 

855i 

8553 

8554 

8556 

4o 

20 

9-997872 

7876  7877  7879;788iJ7883 

39 

20 

9.998668 

856o 

856i 

8563 

8565 

8566 

39 

21 

7885 

7887  7889  78917893  7896 

38 

21 

8568 

857o 

8572 

8573 

8575 

8677 

38 

22 

7897 

7900  7902  7904  7906  7908 

37 

22 

8578 

858o 

8682 

8584 

8585 

8687 

37 

23 

79io 

7912  79x4791679x87^30 

36 

23 

8589 

8690 

8592 

8594 

8595 

8597 

36 

24 

7922 

7924  7926  7929  79°'  ! 

35 

24 

8599 

8601 

8602 

86o4 

8606 

86o7 

35 

25 

7935 

793779397941  79437945 

34 

26 

86o9 

86x1 

8612 

86i4 

8616 

86i7 

34 

26 

7947 

7949  795i  7953  7955  7957 

33 

26 

86i9 

8621 

8622 

8624 

8626 

8627 

33 

27 

7959 

796i  79637965  796^7970 

32 

27 

8629 

863:  8633 

8634 

8636 

8638 

32 

28 
29 

7972 
7984 

7974.79761797879807983 

79867988799079027094 

3i 
3o 

28 

29 

8639 
8649 

- 
865i 

8653 

8644 
8654 

8646  8648 
86568657 

3i 
3o 

3o 

9.997996 

•7998  8000  8002  8oo4  8006  29 

3o 

9.998659 

8661 

8662 

8664 

8666 

8667 

29 

3: 

8008 

8010  8012  8oi4  8016  8018 

28 

3i 

8669 

867r 

86-72 

8674 

8676 

8677 

28 

32 

8020 

8022  8024  8026  8028  8o3o 

27 

32 

8679 

8681 

8682 

8684 

8686 

8687 

27 

33 

8o32 

8o34  8o36  8o38;8o4o  8042  26 

33 

8689 

8690 

8692 

8694 

8695 

8697 

26 

34 

8o44 

8o46  8o48  8060  8062  8o54  26 

34 

8699 

8700 

8702 

8704 

87o5 

8707 

25 

35 

8o56 

8068  8060  8062  8o64  8066  24 

35 

8-708 

8710 

8712 

87i3 

8716 

8717 

24 

36 

8068 

8o7o  %)72  8074  8076  8078  23 

36 

8-718 

8720 

8721 

8723 

8725 

8726 

23 

37 

8080 

8082  8o84  8086  8088  8oy<>  1212 

37 

8728 

8739 

873i 

8733 

8734 

8736 

22 

38 

8092 

8o94  8o96  8o98  8100  8102  21 

38 

8738 

8739 

8741 

8742 

8746 

21 

39 

8io4 

8106810881108112  8114  20 

39 

8747 

8749 

8760 

8762 

8754 

8755 

2O 

4o 

9.998116 

8118  81208122  81248126  19 

4o 

9.998757 

8768 

8760 

8762 

87G-; 

8765 

!9 

4i 

8128 

8i3o8i3i  8i338i358i37  18 

4i 

8766 

8768 

8769 

877J 

8773 

8774 

18 

42 

8i39 

8i4i  8i43  8x45  8147  8i49  17 

42 

8776 

8777 

S779 

8781 

8782 

8784 

J7 

43 

8i5i 

8i538i558i578i598i6i  16 

43 

8786 

S79o 

8793 

6 

44 

8i63 

816581678x6881708179  16 

44 

8795 

8796 

8798 

8799 

88o3 

5 

45 

8i74 

8i76  8178  81808x83  8i84  i4 

45 

88o4 

8806 

8807 

88o9 

8812 

4 

46 

8186 

Ji88  8ioof8i92|8io.4  8i95  i3 

46 

88i3 

8816 

8817 

8818 

8820 

8821 

3 

47 

8i97 

8i99  8201  8203^206  8207  12 

47 

8823 

8826 

8827 

8829 

883i 

2 

48 

8209 

8211  83x3  8sx5  83x7  8318  n 

48 

8832 

8834  8835 

8837 

8838 

884o 

I 

49 

8220 

8222  8224  8226  8228  823o  10 

49 

884i 

8843 

8844 

8846 

8848 

8849 

0 

5o 
5i 

9.998232 
8243 

8234  8236  8238  8239  8241  9 
82458247|8249J835i  8263  8 

5o 
61 

9.99885i 
8860 

8862 
8861 

8854 
8863 

8855 
8864 

8857 
8866 

8858 
8867 

52 

8255 

8267  8258:826oj8262  8264!  7 

62 

8869 

8870 

8872 

8873 

8875 

8877 

7 

53 

8266 

8268  8270  8272  8273  8276 

6 

53 

8878 

8880 

8881  8883 

8884 

8886 

6 

54 

8277 

82798281  8283:8286  8287 

5 

54 

8887 

8889 

88908892 

8893 

8895 

5 

55 

8289 

8290  8292  8294  8296  8298 

4 

55 

8896 

889818899  89oi 

89o2!89o4 

4 

56 

83oo 

83o2  83o3  83o5  8307  8309 

3 

56 

89o5  8907  8908  8910  891  1  Syi  3 

3 

57 

83n 

83i383i583i683i8832o  2 

57 

8914  8916  891-7  8919  8920  8922 

2 

58 

8322 

8324  8326  8328  8329  833i  i 

58 

8923  8926  8926  892-7  8929  8930 

I 

59 

8333 

8335  83378339834i  8342  o 

59 

8932  8933  8935  8936  8938  8939 

O 

60"    ]  50"   40"   30"   20"   10"  ;  . 

60"     50"   40"   30"   20"   10" 

Co-sine  of  5  Decrees.      a 

Co-sine  of  4  Degrees.      a 

P  Part  5  l"  ~"  3"   4"  5"  6"  7"   8"  9//          »P"  2"   3//   4"   5//   6"  7"  8"  *" 

irtj  001111122;;     irtj  0   0   0   1   1   1   1   1   1 

LOGARITHMIC    TANGENTS. 


109 


1 

Tangent  of  84  Degrees. 

j 

Tangent  of  85  Degrees.     | 

X 

0" 

10" 

20" 

30" 

40" 

50" 

a 

0" 

10" 

20" 

30" 

40" 

50") 

0 

10.978380 

8582 

8785 

8988 

9191 

9394 

5o 

0 

n.o58o48 

8291 

8533 

8776 

9019 

9262 

59 

i 

9597 

9800 

...3 

.206 

.4io 

.6i3 

58 

I 

95o6 

9749 

9993 

.236 

.480 

.724 

58 

2 

10.980817 

1021 

1224 

1428 

i632 

i836 

57 

2 

ii  .060968 

1212 

i456 

1701 

1945 

2190 

57 

o 

2O4I 

2245 

2449 

2654 

2858 

3o63 

56 

3 

2435 

2680 

2925 

3170 

34i6  366i 

56 

4 

3268 
4498 

347S 
4703 

3677 
4909 

3882 
5n4 

4o87 
5320 

4293 
5526 

55 

54 

4 
5 

39o7 

5384 

4i53 
563i 

4399 
5877 

4645 
6124 

4891  5i38 
6371  6619 

55 

54 

6 

5732 

5938 

6i44 

635o 

6556 

6763 

53 

6 

6866 

7n3 

736i 

7609 

7857 

8io5 

53 

7 

6969 

7176 

7382 

7589 

7796 

8oo3 

52 

7 

8353 

8601 

885o 

9098 

9347 

9596 

5a 

8 

8210 

84i7 

8624 

883i 

9039 

9246 

5i 

8 

9845 

.-94 

.343 

.593 

.842 

I092j5l 

9 

9454 

9662 

9869 

••77 

.285 

.493 

5o 

9 

II.07l342 

1592 

1842 

2O92 

2343 

2593 

5o 

10 

10.990702 

o9io 

1118 

l327 

i535 

1744 

49 

10 

2844 

3093 

3346 

3597 

3848 

4ioo 

49 

ii 

I953 

2162 

237I 

258o 

2789 

2998 

48 

1  1 

435i 

46o3 

4855 

5io7 

5359'56n 

48 

12 

i3 

3208 
4466 

34i7 
4676 

3627 

4886 

3836 
5o96 

4o46 
53o7 

4256 
55i7 

47 
46 

12 

i3 

5864 
738i 

6116 
7635 

6369 

7888 

6622 
8142 

6875  7128147 
8396865o46 

i4 

5728 

5939 

6149 

636o 

657i 

6-782 

45 

i4 

89o4 

9l59 

94i3 

9668 

9922 

.177 

45 

i5 

6993 

72o5 

74i6 

7627 

7839 

8o5i 

44 

i5 

1  1.  o8o432 

0688 

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1199 

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1710 

44 

16 

17 

8262 
9535 

8474 
9748 

8686 
9960 

8898 
.i73 

9111 
.386 

9323 
•599 

43 

42 

16 

i966 
35o5 

2222 
3762 

2478 
4oi9 

2735 
4276 

299i  3248 
453414791 

43 

42 

18 

ii  .000812 

1025 

1238 

i45i 

1  66  5 

i878 

4i 

18 

5o49 

53o7 

5565 

5823 

6082,6340 

4i 

19 

2092 

23o6 

2519 

2733 

2947 

3i6i 

4o 

ig 

6599 

6858 

7117 

7376 

76357894 

4o 

20 

3376 

359o 

38o4 

4019 

4234 

4448 

39 

20 

8i54 

84i4 

8674 

8934 

91949454 

39 

21 

4663 

4878 

5093 

53o8 

5524 

5739 

38 

21 

97i5 

9975 

.236 

•497 

•  758  1020 

38 

22 

5955 

6i7o 

6386 

6602 

6818 

7o34 

37 

22 

II  .O9I28l 

1  543 

i8o4 

2066 

2328  2590 

37 

23 

725o 

7466 

7682 

7899 

8n5 

8332 

36 

23 

2853 

3n5 

3378 

364  1 

3904 

4167 

36 

24 

8549 

8765 

8982 

9199 

9417 

9634 

35 

24 

443o 

4694 

4957 

5221 

5485 

5749 

35 

25 

>   985i 

..69 

.286 

.5o4 

.722 

.94o 

34 

25 

6oi3 

62-78 

6542 

68o7 

7072 

7337 

34 

26 

ii.oni58 

i376 

i594 

i8i3 

2031 

225o 

33 

26 

7602 

7868 

8i33 

8399 

8665 

893i 

33 

27 

2468 

2687 

2906 

3i25 

3344 

3563 

32 

27 

9197 

9463 

973o 

9996 

.263 

.53o 

32 

28 

3783 

4OO2 

4222 

444  1 

466i 

488i 

3i 

28 

11.100797 

io65 

i332 

1600 

1868 

2i36 

3i 

29 

5ioi 

532i 

554i 

5762 

5982 

6202 

3o 

29 

2404 

2672 

294o 

32O9 

3478 

3747 

3o 

3o 

6423 

6644 

6865 

7o86 

7307 

7628 

29 

3o 

4oi6 

4285 

4555 

4824 

5094 

5364 

29 

3i 

7749 

197  1 

8192 

84i4 

8636 

8857 

28 

3i 

5634 

59o4 

6i75 

6445 

67i6 

6987 

28 

32 

9079 

9524 

9746 

9968 

.191 

27 

32 

7258 

7J29 

78oi 

8o72 

8344 

8616 

27 

33 

o636 

o859 

1082 

i3o5 

i528 

26 

33 

8888 

9i6o 

9433 

97o5 

9978 

.a5i 

26 

34 

1752 

i975 

2199 

2422 

2646 

28-70 

25 

34 

ii  .  no524 

o798 

IO7I 

1  345 

1618 

l892 

25 

35 

3094 

33i8 

3542 

3767 

3991 

4216 

24 

35 

2l67 

244  1 

27l5 

2990 

3265 

354o 

24 

36 

444o 

4665 

4890 

5n5 

534o 

5565 

23 

36 

38i5 

4o9o 

4366 

4642 

4917 

5i93 

23 

37 

5791 

6016 

6242 

6468 

6693 

69i9 

22 

37 

547o 

5746 

6023 

6299 

6576 

6853 

22 

38 

7i45 

7372 

7598 

7824 

8o5i 

8277 

21 

38 

7i3i 

74o8 

7686 

7963 

8241 

8520 

21 

39 

85o4 

873i 

8958 

9i85 

9412 

964o 

20 

39 

8798 

9076 

9355 

9634 

99i3 

.192 

2O 

4o 

9867 

..95 

.322 

.55o 

.778 

1006 

:9 

4o 

ii  .  120471 

o75i 

io3i 

i3n 

1691 

1871 

J9 

4i 

n.o3i234 

1462 

i69i 

1919 

2148 

2377 

18 

4i 

2l5l 

2432 

27l3 

2994 

3275 

3556 

18 

42 

2606 

2835 

3o64 

3293 

3522 

3752 

17 

42 

3838 

4n9 

44oi 

4683 

4966 

5248 

i7 

43 

3981 

4211 

444i 

467i 

4901 

5i3i 

16 

43 

553i 

58i3 

6o96 

638o 

6663  6946 

16 

44 

536i 

5592 

5822 

6o53 

6284 

65i4 

i5 

44 

7230 

75i4 

779s 

8082 

8367 

865i 

i5 

45 

6745 

6977 

•7208 

7439 

7671 

7902 

i4 

45 

8936 

922I 

9792 

••77 

.363 

i4 

46 

8i34 

8366 

8598 

883o 

9062 

9295 

i3 

46 

n.i3o649 

o935 

1221 

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1794 

2081 

i3 

47 

9527 

976o 

9992 

.225 

.458 

.691 

12 

47 

2368 

2656 

2943 

323i 

35i838o6 

12 

48 

11.040925 

ii58 

i39i 

1625 

i859 

2092 

II 

48 

4og4 

4383 

467i 

496o 

5249  5538 

II 

49 

2326 

256i 

2795 

3029 

3264 

3498 

10 

49 

5827 

6n7 

6407 

6697 

6987  7277 

10 

5o 

3733 

3968 

4203 

4438 

4673 

4908 

9 

5o 

7567 

7858 

8149 

844o 

873i!9o23 

9 

5i 

5i44 

5379 

56i5 

585i 

6o87 

6323 

8 

5i 

93i4 

9606 

9898 

.  190 

.483 

.775 

8 

52 

6559 

6795 

7o32 

7268 

75o5 

7742 

7 

52 

11.141068 

i36i 

i654 

i94? 

2241 

2535 

7 

53 

7979 

8216 

8453 

8691 

8928 

9166 

6 

53 

2829 

3i23 

34i7 

3712 

4007 

43oi 

6 

54 

94o3 

9641 

9879 

.117 

.356 

.594 

5 

54 

4597 

4892 

5187 

5483 

5779 

6o75 

5 

55 

n.o5o832 

IO7I 

i3io 

1  549 

1-788 

2027 

4 

55 

6372 

6668 

6965 

7262 

7559|7856 

4 

56 

2266 

25o6 

2745 

2985 

3225 

3465 

3 

56 

8i54 

8452 

875o 

9o48 

9346  9645 

3 

57 

37o5 

3945 

4i85 

4426 

4666 

49o7 

2 

57 

9943 

.242 

.542 

.84i 

ix4i 

i44o 

2 

58 

5i48 

5389 

563o 

5871 

6112 

6354 

I 

58 

n.i5i74o 

2041 

234i 

2642 

2942 

3243 

I 

59 

6596 

6837 

7°79 

7321 

7563 

78o6 

O 

59 

3545  3846  4i48 

4449 

4752  5o54 

O 

60"      50" 

40" 

30" 

20" 

10" 

. 

60"      50"   40"   30"  |  20"   10" 

j 

Co-tangent  of  5  Degrees. 

a 

Co-tangent  of  4  Degrees. 

s 

P  PartJ  1//2"  3"  4"  5"  G//  7"  8//  9" 

(  1"  2"  3"  4"  5"  6"  7"  8"  9" 

P.  Part  ^  27  54  81  log  135  162  188  215  242 

I  10 


LOGARITHMIC    SINES. 


1 

Sine  of  86  Degrees. 

«• 

Sine  of  87  Degrees. 

H 

0" 

10"  1  20" 

!  30"  |  40" 

50" 

s 

0" 

10" 

20" 

30"  |  40" 

50" 

0 

I 

2 

3 

4 

9.998941 

8968 
8967 
8976 

8942|894489458947 
8961  895389648955 
89608961  89638964 
8969  8970  8971  8973 
8977  8979  89808982 

8948 
8967 
8966 
8974 
8983 

69 

58 

ll 

55 

O 
I 

L 

9.999404 
94n 
9418 
9424 
943  1 

94o6 

94l2 

94i9 
9425 
9432 

94o7 
94i3 

94s6 
9433 

94o8 

94i4 

942I 
9427 

9434 

'94o9 
94i5 

9428 
9435 

94io 
94i6 
9423 
943o 
9436 

59 
58 

56 
55 

5 

8984 

8986  8987  8989  899o 

8992 

54 

5 

9437 

9438 

9439 

944o 

944i 

9442 

54 

6 

899389958996 

89978999 

9000 

53 

6 

9443 

9445  9446 

9447 

9448 

9449 

53 

7 

8 

9OO2 

9oio 

9oo3  9oo5 

9OI2  9OI^ 

9006  9007  9oo9 
9oi5  9oi6J9oi7 

62 
5i 

8 

945o 
9456 

945i  9452 
94579458 

9453 
9459 

9454 
946o 

9455 
946i 

62 
5i 

9 

9OI9 

9O2O  9O22 

9023  9024 

9026 

5o 

9 

9463 

9464  9465 

9466 

9467 

9468 

5o 

IO 

9-  999°27 

9o29  9o3o  9o32  9o33 

9o34 

49 

IO 

9  999469 

947o 

947i 

9472 

9473 

9474 

49 

ii 

9o36 

9o37  9o39 

9o4o  9o4i 

9o43 

48 

ii 

9476 

9477 

9478 

9479 

948o 

48 

12 

9044 

9o46  9o47  9o48  9o5o 

9o5i 

47 

12 

948i 

9482 

9483 

9484 

9485 

9486 

47 

i3 

9o53 

9o54  9o55  9067  9o58  9o59 

46 

i3 

9487  9488 

9489 

9490 

949i 

9492 

46 

i4 
i5 
16 

9061 
9069 
9077 

9o62  9o64  9066  9o66  9o68 
9o7i  9o729073j9o759o76 
9079  9o8o  9o82  9o83  9o84 

45 
44 
43 

i4 
16 
16 

9493)9496 
9600  9601 
95o6j95o7 

9496  9497 
9602  9603 
9608  9609 

9498 
95o4 
95io 

9499 
9606 
9611 

45 
44 
43 

17 

9086 

9087  9o88  9o9o  9o9i 

9092 

42 

17 

95i295i3 

95i4 

9616 

95i6 

9617 

42 

18 

9094 

9096  9097  9098 

9099 

9IOI 

4i 

18 

95i8 

95i9 

9620 

9621 

9522 

9523 

4i 

19 

20 

9102 
9.999no 

9io3  9106  9io6  9107 
9111  9ii3|9ii49n5 

9109 
9117 

4o 
39 

'9 

20 

9524 
9.999529 

9525 
953o 

9626 
953i 

9627 
9532 

952? 
9533 

9528 
9534 

4o 
39 

21 

9118 

9I20  9I2I 

9I22 

9124 

9126 

38 

21 

9535 

9536 

9537 

9538 

9539 

954o 

38 

22 

9126 

9I28  9I29 

!9i3o 

9l32 

9133 

37 

22 

954i 

9542 

9543 

9544 

9545 

9546 

37 

23 

9i34 

9i369i379i38 

9i4o 

9141 

36 

23 

9547 

9548 

9549 

9660 

955i 

9552 

36 

24 

9i42 

9i43  9i45  9i46 

9i47 

9i49 

35 

24 

9553 

9554 

9555 

9556 

9557 

9557 

35 

25 

9160 

9i5i  9i53  9164 

9i55 

9l57 

34 

25 

9558 

9559 

9660 

9661 

9662 

9563 

34 

26 

9168 

9i59  9i6i 

9l62 

9i63 

9i65 

33 

26 

9564 

9565 

9666 

9667 

9668 

9569 

33 

27 

9166 

9i67  9168  9170 

9i7i 

9I72 

32 

27 

957o 

957i 

9572 

9573 

9573 

9574 

3a 

28 

9i74 

9176  9176  9178 

9179 

9180 

3i 

28 

9575 

9676 

9677 

9678 

9579 

958o 

3i 

29    9181 

9i839i84 

9i85 

91879188 

3c 

29 

958i 

9682 

9683 

Q584 

9585 

9586 

3o 

3o  7.999189 

91909192  9193 

91949196 

29 

3o 

9.999686 

9687 

9688 

9589 

959o 

959i 

29 

3i 

9197 

9i98  9i99  9201 

9202  9203 

28 

3i 

9692 

9593 

9594 

9696 

9596 

9597 

28 

32 

9206 

9206  9207  9208 

92109211 

27 

32 

9697 

9698 

9599 

9600 

9601 

96o2 

27 

33 

9212 

9213  9215  9216 

92I7 

9219 

26 

33 

9603 

9604 

96o5 

9606 

9606 

9607 

26 

34 

9220 

9221  9222  9224 

9225 

9226 

25 

34 

9608 

96o9 

96io 

9611 

9612 

96:3 

25 

35 

9227 

9229  9230  9231 

92329234 

24 

35 

9614 

9614 

96i5 

9616 

96i7 

96i8 

24 

36 

9s35 

92369237 

9239 

924l 

23 

36 

9619 

9620 

962I 

9622 

9622 

9623 

23 

3? 

9242 

9244924^9246 

0°47 

9249 

22 

37 

9624 

9625 

9626 

0627 

9628 

9629 

22 

38 

9260 

9261  9262  9254 

9266  9256 

21 

38 

9629 

963o 

963i 

9632 

9633 

9634 

21 

39 

9267 

9258  9260  9261 

9262 

9263 

2O 

39 

9635 

9635 

9636 

9632 

9638 

9639 

20 

4o 

9.999265 

9266  926719268 

9270 

9271 

I9 

4o 

9.9996409641 

964i 

9643 

9644 

IQ 

4i 

42 

9272 
9279 

9273  92749276 
92809282  9283 

9277,9278 
9284,9286 

18 

17 

4i 

42 

9645  9646 
96609661 

9647 
9652 

9647 
9653 

9648 
9653 

9649 
9654 

18 

43 

9287 

9288  928919290 

9291 

9293 

16 

43 

9666 

9656 

9667 

9668 

9658 

9659 

16 

44 

9294 

9295  9296  9297 

9299  93oo 

i5 

44 

9660 

966il9662 

9663  9663 

9664 

16 

45 

93oi 

9302  93o3 

93o5 

93o693o7 

i4 

45 

9666 

9666 

9667 

9668  9668]Q669 

i4 

46 

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93i3|93i4 

i3 

46 

9670 

967i 

9672 

9672 

9673 

9674 

i3 

47 
48 

93i5 
9322 

93i6  9318  9319 
932393269326 

9320932I 

12 

47 
48 

967696769677 
9680968119681 

9677  9678  9679 
9682  9683  9684 

12 
II 

49 

9329 

933i  93329333 

9334!9335 

IO 

49 

968696869686 

968796889689 

10 

5o 

9  999336 

9338  9339  9340 

934i 

9342 

9 

5o 

9.99968996909691 

9692 

9693 

9693 

9 

5i 

9343 

9344  9346  9347 

9348  9349 

8 

5i 

9694  9695  9696 

9697 

9697 

9698 

8 

52 

935o 

935i  9353 

9354 

93559356 

7 

62 

9699  9700  97oo 

9701 

9702 

97o3 

7 

53 

9357 

93589359 

936i 

93629363 

6 

53 

9704  9704  97o5  9706 

97°7 

9707 

6 

54 

9364 

93659366 

9367 

93699370 

5 

54 

97o8j97o9j97io  97i  i 

9711 

9712 

5 

55 

937i 

9372'93739374 

9376.9377 

4 

55 

97i3  97i4  97*4  9716 

9716 

91*7 

4 

56 

9378 

9379'938o938i 

93829383 

3 

56 

9717 

97l8  97I9  9720  9720 

972i 

3 

57 

9384 

9385;93879388 

9389  939o 

2 

57 

9722  9723  9723  9724  9725 

9726 

2 

58 

939i 

939293939394 

93969397 

I 

58 

9726  9727  Q728  9729  9729  973o 

I 

59 

9398 

9399!94oo  94oi 

94o2  94o3 

O 

59 

973i[9732  9732  9733  9734  9735 

O 

60" 

50"  j  40" 

30"   20" 

10" 

. 

CO"     50"   40"   30"   20"  |  10" 

. 

Co-sine  of  3  Degrees. 

§ 

Co-sine  of  2  Degrees. 

i 

r-Ho'  1  3o'  v 

5"  6"  7" 
1   1   1 

8"  9" 
1   1 

p  p  .  C  1"  2"  3"  4"  5"  6"  7"  V  9" 

in\  000001111 

LOGARITHMIC    TANGENTS. 


1  1  1 


.5 

Tangent  of  86  Degrees. 

d 

Tangent  of  87  Degrees. 

*% 

0" 

10" 

20" 

30" 

40" 

50" 

2 

0" 

10" 

20" 

30" 

40" 

50" 

0 

1  1.  155356 

5659 

5962 

6265 

6568 

6872 

59 

0 

11.280604 

IOO7 

i4n 

1814 

22I9 

2623 

59 

I 

7i75 

7479 

7784 

8088 

8393 

8697 

58 

I 

3oa8 

3433 

3839 

4245 

4652 

5o58 

58 

2 

9002 

93o8 

9613 

9919 

.224 

.53o 

57 

2 

5466 

5873 

6281 

6689 

7o98 

75o7 

57 

3 

11.160837 

n43 

i45o 

1757 

2064 

237I 

56 

3 

79i7 

8326 

8737 

9i47 

9558 

9970 

56 

4 

2679 

2987 

3295 

36o3 

39n 

4220 

55 

4 

zz.  990882 

o794 

1206 

1619 

2o33 

2446 

55 

5 

4529 

4838 

5i47 

5457 

5766 

6o76 

54 

5 

2860 

3275 

3690 

4io5 

452i 

4937 

54 

6 

6387 

6697 

•7008 

73i8 

7629 

794  1 

53 

6 

5354 

577o 

6188 

66o5 

•7024 

7442 

53 

7 

8252 

8564 

8876 

9188 

95oo 

98i3 

52 

7 

7861 

8280 

8700 

9120 

954i 

9962 

52 

8 

ii  .  170126 

o439 

O7f>2 

1066 

i379 

i693 

5i 

8 

ii.3oo383 

o8o5 

1227 

1649 

2072 

2496 

5i 

9 

2008 

2322 

2637 

295i 

8267 

3582 

5o 

9 

29i9 

3344 

3768 

4i93 

46i9 

5o44 

5o 

10 

3897 

42i3 

4529 

4845 

5i62 

5478 

49 

10 

547i 

5897 

6325 

6752 

7i8o 

•7608 

49 

1  1 

5795 

6112 

643o 

6747 

7o65 

7383 

48 

ii 

8o37 

8466 

8896 

9326 

9756 

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48 

12 

7702 

8020 

8339 

8658 

8977 

9T97 

47 

12 

11.3/0619 

io5o 

i483 

1915 

2348 

2782 

47 

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9616 

9936 

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1218 

46 

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32i6 

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ii.  181539 

1860 

2182 

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45 

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5828 

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i5 

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3793 

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44 

16 

54n 

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43 

16 

ii  .3  tnoo 

1  543 

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43 

1? 

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801  1 

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42 

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3761 

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465i 

5°97 

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42 

18 

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9971 

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•  954 

4i 

18 

6437 

6885 

7333 

7782 

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11.191283 

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2598 

2928 

4o 

J9 

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958i 

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^35 

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20 

3258 

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39 

20 

n.J.Vi84o 

2293 

2747 

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3B56 

4izi 

39 

21 

6242 

5573 

6905 

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6569 

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38 

21 

4867 

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5480 

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38 

22 

7235 

7568 

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8568 

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37 

22 

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37 

23 

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36 

23 

1  1  .  ?-4ooy2 

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24 

II  .201248 

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35 

24 

285i 

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5i8o 

35 

25 

3269 

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3944 

4282 

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34 

25 

5648 

6116 

6584 

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34 

26 

5299 

5638 

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33 

26 

8463 

8933 

94o5 

9877 

•  349 

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33 

27 

7338 

7679 

8020 

836i 

87o3 

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32 

27 

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28 

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3i 

28 

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3i 

29 

n.2ix446 

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2134 

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2823 

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29 

7018 

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4206 

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29 

3o 

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•  874 

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1  844 

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29 

3i 

5592 

5939 

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6635 

6983 

733i 

28 

3i 

ii  .862816 

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3789 

4277 

4765 

5254 

28 

32 

768o 

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27 

32 

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27 

33 

9779 

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26 

33 

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1164 

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34 

11.321886 

2239 

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2944 

3298 

365i 

25 

34 

11,371660 

2i56 

2654 

3i5i 

365o 

4i4g 

25 

35 

4oo5 

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5423 

5778 

24 

35 

4648 

5i48 

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6i5o 

6652 

7i54 

24 

36 

6i34 

6489 

6845 

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23 

36 

7657 

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91-70 

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23 

3? 

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22 

37 

n.38o687 

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38 

ii  .a3o422 

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21 

38 

3738 

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39 

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20 

39 

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8396 

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18 

4i 

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5637 

18 

4s 

9I28 

9495 

9861 

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•  964 

ll 

42 

6161 

6687 

7213 

774o 

826? 

8795 

17 

43 

n.a4i33a 

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2069 

2438 

28o7 

3i77 

16 

43 

9323 

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1  444 

1976 

16 

44 

3547 

39i7 

4288 

4659 

5o3o 

54oi 

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44 

Ii.4o25o8 

3o4i 

3575 

4no 

4645 

5i8o 

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45 

5773 

6i45 

65i8 

689i 

•7264 

7637 

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45 

57i7 

6254 

6792 

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7869 

84o9 

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46 

Son 

8385 

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46 

894Q 

949o 

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•  574 

1117 

1661 

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4? 

ii  .250260 

o636 

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i389 

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2143 

12 

47 

II.4l22o5 

275l 

3296 

3843 

439o 

4938 

12 

48 

2521 

2899 

3277 

3656 

4o34 

44i4 

II 

48 

5486 

6o3fi 

6586 

7i36 

7688 

8240 

II 

49 

4793 

5i73 

5553 

5934 

63i5 

6696 

IO 

49 

6792 

q346 

990o 

Xf^ 

IOIO 

i566 

10 

5o 

7o78 

746o 

784a 

822^ 

86o7 

899i 

9 

5o 

II  .422123 

2681 

3a4o|3799 

4358 

4919 

9 

5i 

9374 

9758 

.142 

.527 

.912 

I297 

8 

5i 

548o!6o42 

66o5|7i68 

7733 

8298 

8 

52 

ii.  26i683 

2o69 

2455 

2842 

3229 

36i6 

7 

52 

8863 

943o 

9997 

.565 

n33 

1702 

7 

53 

4oo4 

4392 

478o 

5i69 

5558 

5947 

6 

53 

11.432273 

2843 

34i5 

3987|456o 

5i34 

6 

54 

6337 

6727 

7117 

75o8 

7899 

829I 

5 

54 

57o9 

6284 

6860 

7437 

8016 

8593 

5 

55 

8683 

9o75 

9467 

986o 

.254 

.647 

4 

55 

9I72 

9752 

.333 

.9i5 

1497 

2080  4 

56 

11.971041 

1435 

i83o 

2225 

2620 

3oi6 

3 

56 

11.442664 

3248 

3834 

4420 

5oo7 

5595 

3 

57 

58 

3412 

5796 

3809 
6195 

4206 
6594 

46o3 
6993 

5ooo 
7393 

5398 
7793 

2 
I 

57 
58 

6i83 

9732 

6773 
.326 

736379548546 

.92Ijl5l7  21  l2 

9i38 
2711. 

2 
I 

59 

8i94 

85958996 

9397 

9799 

.202 

0 

59 

II.453309 

39o845o8|5io9!57ii 

63i3 

o 

60" 

50"   40" 

30"  |  20"  |  10"   A 

60"     50"  |  40"   30"   20" 

10" 

JL 

Co-tangent  of  3  Degrees. 

i 

Co-tangent  of  2  Degrees. 

s 

p  p   <  1"  2"  3"  4"  5"  6"  7"  8"  9"  1       (  1"  2"  3"  4"  5"  6"  7"  8"  9" 
}  35  69  104  138  173  207  242  276  311  |     ir  \  48  97  145  193  242  290  338  387  435 

112 


LOGARITHMIC    SINES. 


1 

Sine  of  88  Degrees. 

.a 

Sine  of  89  Degrees. 

• 

0" 

10" 

20" 

30" 

40" 

50" 

m 

0" 

10" 

20" 

30" 

40" 

50" 

o 

9-999735 

9736 

9737 

9738 

9738 

9739 

59 

0 

9.999934 

9934 

9935 

9935 

9935 

9936 

59 

I 

974o 

974o 

974i 

9742 

9743 

9743 

58 

i 

9936 

9936 

9937 

9937 

9937 

9938 

58 

2 

9744 

9745 

9746 

9746 

9747 

9748 

57 

2 

9938 

9939 

9939 

9939 

994o 

994o 

57 

3 

9748 

9749 

975o 

975i 

975i 

9752 

56 

3 

994o 

994i 

994i 

994i 

9942 

9942 

56 

4 

9753 

9753 

9754 

9755 

9756 

9756 

55 

4 

9943 

9943 

9943 

9944 

9944 

55 

5 

9757 

9758 

9758 

9759 

9760 

9760 

54 

5 

9944 

9945 

9945 

9945 

9946 

9946 

54 

6 

976i 

9762 

9763 

9763 

9764 

9765 

53 

6 

9946 

9947 

9947 

9947 

9948 

9948 

53 

7 

9765 

9766 

9.767 

9767 

9768 

9769 

52 

7 

9948 

9949 

9949 

9949 

995o 

995o 

52 

8 

9769 

9770 

9771 

9772 

9772 

9773 

5i 

8 

995o 

995i 

995i 

995i 

9952 

9952 

5i 

9 

9774 

9774 

9775 

9776 

9776 

9777 

5o 

9 

9952 

9953 

9953 

9953 

9953 

9954 

5o 

IO 

9-999778 

9778 

9779 

0.780 

9780 

9781 

49 

IO 

9954 

9955 

9955 

9955 

9956 

49 

ii 

0782 

9782 

9783 

9784 

9784 

9785 

48 

ii 

9956 

9956 

9956 

9957 

9957 

9957 

48 

12 

9786 

9786 

9787 

9788 

9788 

9789 

47 

12 

9958 

9958 

9958 

9959 

9959 

9959 

47 

i3 

979° 

979° 

9791 

979s 

9792 

9793 

46 

i3 

9959 

9960 

996o 

996o 

996i 

996i 

46 

i4 

9794 

9794 

9795 

9795 

9796 

9797 

45 

i4 

996i 

9961 

9962 

9962 

9962 

9963 

45 

i5 

9797 

9798 

9799 

9799 

9800 

98oi 

44 

i5 

9963 

9963 

9963 

9964 

9964 

9o64 

44 

16 

9801 

9802 

98o3 

98o3 

9804 

98o4 

43 

16 

9964 

9965 

9965 

9965 

9965 

9,9,66 

43 

17 

9805 

9806 

98o6  98o7 

9808 

9808 

42 

17 

9966 

9966 

9967 

9967 

9967 

9967 

42 

18 

9809 

9809 

98io98n 

9811 

98l2 

4i 

9968 

9968 

9968 

9968 

9969 

9969 

4i 

i9 

9813 

9813 

98i498i4 

98i5 

98i6 

4o 

i9 

9969 

9969 

9970 

997° 

997° 

997° 

4o 

20 

9.999816 

9817 

98i798i8 

9819 

9819 

39 

20 

9-999971 

9971 

9971 

9971 

9972 

9972 

39 

21 

9820 

9820 

9821  9822 

9822 

9823 

38 

21 

9972 

9972 

9973 

9973 

9973 

9973 

38 

22 

9824 

9824 

9825(9825 

9826 

0827 

37 

22 

9973 

9974 

9974 

9974 

9974 

9975 

37 

23 

9827 

9828 

98289829 

9829 

983o 

36 

23 

9975 

9975 

9975 

9976 

9976 

9976 

36 

24 

983i 

983i 

9832|9832 

9833 

9834 

35 

24 

9976 

9976 

9977 

9977 

9977 

9977 

35 

25 

9834 

9835 

9835|9836 

9836 

9837 

34 

25 

9977 

9978 

9978 

9978 

9978 

9979 

34 

26 

9838 

9838 

9839'9839 

984o 

984o 

33 

26 

9979 

9979 

9979 

9979 

998o 

9980 

33 

27 

984i 

9842 

9842'9843 

9843 

9844 

32 

27 

998o 

9980 

9980 

9981 

998i 

9981 

32 

28 

9844 

9845 

9846i9846 

9847 

9847 

3i 

28 

998i 

9982 

9982 

9982 

9982 

3i 

29 

9848 

9848 

9849!9849 

985o 

985i 

3o 

29 

9982 

9983 

9983 

9983 

9983 

9983 

3o 

3o 

9.99985i 

9852 

9852:9853 

9853 

9854 

29 

3o 

9.999983 

9984 

9984 

9984 

9984 

9984 

29 

3i 

9854 

9855 

98569856 

9857 

9857 

28 

3i 

9985 

9985 

9985 

9985 

9985 

9985 

28 

32 

9858 

9858 

9859*9859 

986o 

986o 

27 

32 

9986 

9986 

9986 

9986 

9986 

9986 

27 

33 

986i 

9861 

9862  9863 

9863 

9864 

26 

33 

9987 

9987 

9987 

9987 

9987 

9987 

26 

34 

9864 

9865 

9865  9866 

9866 

9867 

25 

34 

9988 

9988 

9988 

9988 

9988 

9988 

25 

35 

9867 

9868 

98689869 

9869 

9870 

24 

35 

9989 

9989 

9989 

9989 

9989 

9989 

24 

36 

987o 

9871 

9871  9872 

9872 

9873 

23 

36 

9989 

999° 

9990 

999° 

999° 

999° 

23 

37 

9873 

9874 

98749875 

9875 

9876 

22 

37 

999° 

999° 

999  * 

9991 

9991 

9991 

22 

38 

9876 

9877 

9877,9878 

9878 

9879 

21 

38 

999  i 

9991 

9991 

9992 

9992 

9992 

21 

39 

9879 

9880 

9880  9881 

988i 

0882 

2O 

39 

9992 

9992 

9992 

9992 

9992 

9993 

2O 

4o 

9.999882 

9883 

98839884 

9884 

9885 

'9 

4o 

9-999993 

9993 

9993 

9993 

9993 

9993 

*9 

4i 

9885 

9886 

98869887 

9887 

9888 

18 

4i 

9993 

9993 

9994 

9994 

9994 

9994 

18 

42 

9888 

9889 

9889  9890 

989o 

9891 

17 

42 

9994 

9994 

9994 

9994 

9994 

9995 

17 

43 
44 
45 

9891 
9894 
9897 

9892 
9894 
9897 

9892  9892  9893 
989598959896 
9898  9898  9898 

9893 
9896 
9899 

16 
i5 
i4 

43 
44 
45 

9995 
9995 
9996 

9995 
9995 
9996 

9995 
9995 
9996 

9995 
9996 
9996 

9995 
9996 
9996 

9995 
9996 
9996 

16 
i5 
i4 

46 

9899 

9900 

99oo  99oi 

99oi 

9902 

i3 

46 

9996 

9996 

9997 

9997 

9997 

9997 

i3 

47 

99O2 

99°3 

99o3  9903  9904 

99o4 

12 

47 

9997 

9997 

9997 

9997 

9997 

9997 

12 

48 

99o5 

99o5 

9906  9906  9906 

99°7 

II 

48 

9997 

9997 

9997 

9998 

999s 

9998 

II 

49 

99°7 

9908 

9908  9909 

99°9 

99io 

IO 

49 

9998 

9998 

9998 

9998 

9998 

9998 

10 

5o 

9-999910 

9910 

9911  9911 

9912 

99I2 

9 

5o 

9-999998 

9998 

9998 

9998 

999s 

9998 

9 

5i 

52 

99i3 
99i5 

99I3 
99i5 

99139914 
9916  9916 

99i4 
9917 

99i5 
99i7 

7 

5i 

52 

9999 
9999 

9999 
9999 

9999 
9999 

9999 
9999 

9999 
9999 

9999 
9999 

8 
7 

53 

99i8 

99i8 

9918 

9919 

9919 

9920 

6 

53 

9999 

9999 

9999 

9999 

9999 

9999 

6 

54 

992O 

9920 

9921 

9921 

9922 

9922 

5 

54 

9999 

9999 

9999 

9999 

9999 

5 

55 

9922 

9923 

9923 

9924 

9924 

9924 

4 

55 

o.oooooo 

oooo 

oooo 

oooo 

oooo 

oooo 

4 

56 

9925 

9925 

9926 

9926 

9926 

9927 

3 

56 

oooo 

oooo 

oooo 

oooo 

oooo 

oooo 

3 

57 

9927 

9927 

9928 

99289929 

9929 

2 

57 

oooo 

oooo 

oooo 

oooo 

oooo 

oooo 

2 

58 

9929 

9930 

993o 

993i  993i 

993i 

I 

58 

oooo 

oooo 

oooo 

oooo 

oooo 

oooo 

I 

59 

9932 

9932 

9932 

9933|9933 

9933 

O 

59 

oooo 

oooo 

oooo 

oooo 

oooo 

oooo 

0 

60" 

50" 

40" 

30"   20" 

10" 

. 

60" 

50" 

40" 

30" 

20" 

10" 

d 

Co-sine  of  1  Degree. 

S 

Co-sine  of  0  Degree. 

.3 

s 

.(  1"  2"  3"  4"  5"  6"  7''  8"  9" 
1  $0000   00   001 

p  p  .<  1"  2"  3"  4"  5"  6"  7"  8"  9" 

irl  Jo  ooo  oo  ooo 

LOGARITHMIC    TANGENTS. 


1 

Tangent  of  88  Degrees. 

P.  Part 

7Z 

0" 

10" 

20" 

30" 

40" 

50" 

tol". 

o 

11.456916 

ii  .457520 

ii.  458i25 

II.45873I 

n.45|338 

11.459945 

59 

60.6 

I 

46o553 

46n63 

46i773 

462383 

46^905 

4636o8 

58 

61.1 

2 

464221 

464836 

46545i 

466067 

466684 

4673o2 

57 

61.6 

3 

467920 

46854o 

469160 

469782 

47o4o4 

47I027 

56 

62.2 

4 

47i65i 

472276 

472902 

473528 

474i56 

474785 

55 

62.  7 

5 

4754i4 

476044 

476676 

4773o8 

4779^1 

478575 

54 

63.3 

6 

479210' 

479846 

480482 

481120 

481759 

482398 

53 

63.8 

7 

483o39 

48368o 

484323 

484966 

4856n 

486256 

52 

64.4 

8 

486902 

487549 

488198 

488847 

489497 

490148 

5i 

65.o 

9 

490800 

49i453 

492107 

492762 

493418 

494o75 

5o 

65.5 

10 

H.494733 

11.495392 

ii  .496052 

11.496713 

11.497375 

11.498038 

49 

66.1 

ii 

498702 

499367 

5ooo33 

500700 

5oi368 

5o2o37 

48 

66.8 

12 

502707 

5o3378 

5o4o5i 

5o4724 

5o5398 

5o6o73 

47 

67^4 

i3 

506750 

507427 

5o8io6 

5o8785 

5o9466 

5ioi48 

46 

68.0 

i4 

5io83o 

5u5i4 

512199 

5i2885 

5i3572 

514260 

45 

68.6 

i5 

5i4g5o 

5i564o 

5i633i 

5i7o24 

517717 

5i84i2 

44 

69.3 

16 

519108 

519805 

52o5o3 

52I2O2 

521903 

522604 

43 

7o.o 

J7 

523307 

524oio 

5247i5 

525421 

526128 

526837 

42 

7°  -7 

18 

527546 

528257 

528969 

529682 

53o396 

53iin 

4i 

7i.i 

'9 

53i828 

532545 

533264 

533984 

5347o5 

535428 

4o 

72.1 

20 

n.536i5i 

11.536876 

11.537602 

ii.53833o 

ii.  539058 

11.539-788 

39 

72.8 

21 

54o5i9 

54i25i 

541984 

5427i9 

543455 

544192 

38 

73.5 

22 

54493o 

54567o 

5464n 

547i53 

547896 

54864i 

37 

74.3 

23 

549387 

55oi34 

55o883 

55i632 

552384 

553i36 

36 

75.0 

24 

553890 

554645 

5554oi 

556i59 

556918 

557678 

35 

75.8 

25 

55844o 

559203 

559967 

56o733 

56i5oo 

562268 

34 

76.6 

26 

563o38 

563809 

56458i 

565355 

566  i  3o 

5669O7 

33 

77.5 

27 

567685 

568464 

569245 

57OO27 

57o8n 

57i596 

32 

78.3 

28 

572382 

573i7o 

573959 

57475o 

575542 

576336 

3i 

79.i 

29 

577I3i 

5779*8 

578726 

579525 

58o326 

58ii28 

3o 

80.0 

3o 

11.581932 

n.582737 

n.583544 

n.584353 

n.585i63 

n.585974 

29 

80.9 

3i 

586787 

5876-01 

5884i7 

589235 

590054 

5908-74 

28 

81.8 

32 

591696 

592520 

593345 

594172 

595000 

59583o 

27 

82.8 

33 

596662 

597495 

SgSSSo 

599166 

6oooo4 

6oo844 

26 

83.7 

34 

6oi685 

602528 

603372 

604218 

6o5o66 

605915 

25 

84.  7 

35 

606766 

6o76i9 

608474 

609330 

6ioi87 

6iio47 

24 

85.7 

36 

611908 

6i277i 

6i3636 

6i45o2 

6i537o 

616240 

23 

86.7 

3? 

617111 

61-7985 

618860 

6i9737 

620615 

621496 

22 

87.8 

38 

622378 

623262 

624147 

625o35 

625924 

626815 

21 

88.8 

39 

627708 

628603 

629500 

630399 

631299 

6322OI 

2O 

89.9 

4o 

n.633io5 

ii  .634oi2 

ii  .634919 

11.635829 

n.63674i 

n.637655 

I9 

91.1 

4i 

638570 

639488 

640407 

64i329 

642252 

643i77 

18 

92.2 

42 

644io5 

645o34 

645965 

646899 

647834 

64877i 

J7 

93.4 

43 

649711 

65o652 

65i595 

65254i 

653488 

654438 

16 

94.6 

44 

655390 

656343 

657299 

658257 

6592i7 

6601-79 

i5 

95.9 

45 

66u44 

662110 

663079 

664o5o 

665o23 

665998 

i4 

97-2 

46 

666975 

667<}55 

668936 

669920 

67O9O7 

6-71895 

i3 

98.5 

4? 

672886 

673579 

674874 

675871 

676871 

677873 

12 

oo.  8 

48 

678878 

679885 

680894 

681905 

682919 

683935 

II 

loi.S 

49 

684954 

685975 

686998 

688024 

689052 

690083 

IO 

102.7 

5o 

ii  .691  116 

11.692151 

ii  .693189 

ii  .694230 

11.695273 

11.696318 

9 

104.2 

5i 

697366 

698417 

699470 

700526 

7oi584 

-702645 

8 

105.7 

52 

703708 

704774 

705843 

706914 

707988 

•709065 

7 

107.2 

53 

710144 

•711226 

712311 

713398 

714488 

7i558i 

6 

108.9 

54 

716677 

7i7775 

718876 

719980 

721087 

-722196 

5 

no.  5 

55 

723309 

724424 

725542 

726663 

727787 

-728914 

4 

112  2 

56 

73oo44 

731176 

7323i2 

73345i 

734592 

735737 

3 

ii4-o 

5? 

736885 

738o35 

739i89 

74o346 

74i5o6 

-742669 

2 

ii5.8 

58 

743835 

745oo4 

746177 

747352 

74853i 

74971  3 

I 

117.7 

59 

750898 

752087 

753279 

754474 

755672 

756874 

0 

119.7 

60" 

50"         40" 

30"         20"         10" 

. 

Co-tangent  of  1  Degree. 

§ 

1 

114 


AUXILIARY    TABLE   FOR   SINES,   &  c. 


1 

1 

0  Degree. 

1 

1 

1  Degree. 

I 

1 

log.  sin.  A— 
log.  A". 

log.  tan.  A  — 
log.  A". 

log.  cot  A+ 
log.  A". 

1 

i 

log.  sin.  A  — 
log.  A". 

log.  tan.  A— 
log.  A". 

log.  cot  A+ 
log.  A". 

o 

0 

4.685575 

4.685575 

i5.3i4425 

60 

36oo 

0 

4.685553 

4.685619 

i5.3i438i 

60 

60 

I 

575 

575 

425 

59 

366o 

I 

552 

620 

38o 

59 

120 

2 

575 

575 

425 

58 

3720 

2 

55i 

622 

378 

58 

1  80 

3 

575 

575 

425 

57 

378o 

3 

55i 

623 

377 

57 

240 

4 

575 

575 

425 

56 

384o 

4 

55o 

625 

375 

56 

3oo 

5 

575 

575 

425 

55 

3900 

5 

549 

627 

373 

55 

36o 

6 

575 

575 

425 

54 

3960 

6 

548 

628 

372 

54 

420 

7 

575 

575 

4*5 

53 

4020 

7 

547 

63o 

37o 

53 

48o 

8 

574 

576 

424 

52 

4o8o 

8 

547 

632]     368 

52 

54o 

9 

574 

576 

424 

5i 

4i4o 

9 

546 

6331     36? 

5i 

600 

10 

4.685574 

4.685576 

i5.3i4424 

5o 

4200 

10 

4.685545 

4.685635 

i5.3i4365 

5o 

660 

ii 

574 

576 

424 

49 

4260 

ii 

544 

637 

363 

49 

720 

12 

574 

577 

423 

48 

4320 

12 

543 

638 

362 

48 

780 

i3 

574 

577 

423 

47 

438o 

1  3     542 

64o 

36o 

47 

84o 

i4 

574 

577 

423 

46 

444o 

i4 

54i 

642 

358 

46 

900 

i5 

573 

578 

422 

45 

45oo 

i5 

54o 

644 

356 

45 

960 

16 

573 

578 

422 

44 

456o 

16 

539 

646 

354 

44 

IO2O 

r7 

573 

578 

422 

43 

4620 

17 

539 

647 

353 

43 

I080 

18 

573 

579 

421 

42 

468o 

18 

538 

649 

35i 

42 

n4o 

i9 

573 

579 

421 

4i 

474o 

'9 

537 

65i 

349 

4i 

1  200 

20 

4.685572 

4.68558o 

i5.3i442o 

4o 

48oo 

20 

4.685536 

4.685653 

i5.3i4347 

4o 

1260 

21 

572 

58o 

420 

39 

486o 

21 

535 

655 

345 

39 

1320 

22 

572 

58i 

4i9 

38 

4920 

22 

534 

657 

343 

38 

i38o 

23 

572 

58i 

4i9 

37 

4980 

23 

533 

659 

34i 

37 

i44o 

24 

57i 

582 

4i8 

36 

5o4o 

24 

532 

661 

•339 

36 

i5oo 

25 

57i 

583 

417 

35 

5ioo 

25 

53i 

663 

337 

35 

i56o 

26 

57i 

583 

4i7 

34 

5i6o 

26 

53o 

665 

335 

34 

1620 

27 

57o 

584 

4i6 

33 

5220 

27 

529 

668 

332 

33 

1680 

28 

57o 

584 

4x6 

32 

5280 

28 

527 

670 

33o 

32 

1740 

29 

57o 

585 

4x5 

3i 

534o 

29 

526 

672 

328 

3i 

1800 

3o 

4.685569 

4.685586 

i5.3i44i4 

3o 

54oo 

3o 

4.685525 

4.685674 

i5.3i4326 

3o 

1860 

3i 

569 

587 

4x3 

29 

546o 

3i 

524 

676 

324 

29 

1920 

32 

569 

587 

4x3 

28 

5520 

32 

523 

679 

321 

28 

1980 

33 

568 

588 

4X9 

27 

558o 

33 

522 

681 

3i9 

27 

2O4O 

34 

568 

589 

4n 

26 

564o 

34 

521 

683 

3i7 

26 

2IOO 

35 

567 

59o 

4io 

25 

5700 

35 

520 

685 

3i5 

25 

2l6o 

36 

567 

59i 

4o9 

24 

576o 

36 

5i8 

688 

312 

24 

2220 

37 

566 

592 

4o8 

23 

5820 

3? 

5i7 

690 

3io 

23 

2280 

38 

566 

593 

407 

22 

588o 

38 

5i6 

693 

3o7 

22 

234o 

39 

566 

593 

407 

21 

5940 

39 

5i5 

695 

3o5 

21 

s4oo 

4o 

4.685565 

4.685594 

i5.3i44o6 

2O 

6000 

4o 

4.6855i4 

4.685697 

i5.3i43o3 

2O 

2460 

4i 

565 

595 

4o5 

'9 

6060 

4i 

5I2 

700 

3oo 

'9 

2520 

42 

564 

596 

4o4 

18 

6120 

42 

5n 

702 

298 

18 

258o 

43 

564 

598 

4O2 

17 

6180 

43 

5io 

7o5 

295 

17 

2640 

44 

563 

599 

4oi 

16 

6240 

44 

5o9 

707 

293 

16 

2700 

45 

562 

600 

4oo 

i5 

63oo 

45 

5o7 

710 

290 

i5 

2760 

46 

562 

601 

399 

i4 

636o 

46 

5o6 

7i3 

287 

i4 

2820 

47 

56i 

602 

398 

i3 

6420 

47 

5o5 

7i5 

285 

i3 

2880 

48 

56i 

6o3 

397 

12 

648o 

48 

5o3 

718 

282 

12 

2940 

49 

56o 

6o4 

396 

II 

654o 

49 

502 

720 

280 

I  I 

3ooo 

5o 

4.68556o 

4.6856o5 

i5.3i4395 

10 

6600 

5o 

4.6855oi 

4.685723 

i5.  314277 

10 

3o6o 

5i 

559 

607 

393 

9 

6660 

Si 

499 

726 

274 

9 

3l20 

52 

558 

608 

392 

8 

6720 

52|    498 

729 

271 

8 

3i8o 

53 

558 

6o9 

39i 

7 

6780 

53 

497     73i 

269 

7 

8240 

54 

557 

6x1 

389 

6 

684o 

54 

495 

734 

266 

6 

33oo 

55 

556 

612 

388 

5 

6900 

55 

494 

737 

263 

5 

336o 

56 

556 

6i3 

387 

4 

6960 

56     492 

740 

260 

4 

3420 

57 

555 

6i5 

385 

3 

7020 

57 

491 

743 

257 

3 

348o 

58 

554 

616 

384 

2 

7080 

58 

490 

745 

255 

2 

354o 

59     554 

618 

382 

I 

7140 

59 

488 

748 

252 

I 

'log.  cos.  A  — 

log.  eot  A— 

log.  tan,  A-f 

* 

log.  co§.  A  —  log.  cot  A  — 

log.  tan.  A+ 

• 

log.  c.  A". 

log.  c.  A". 

log.  c.  A." 

1 

log.  c.  A". 

log.  c.  A". 

log.  c.  A". 

• 
s 

89  Degrees. 

.9 

53 

88  Degrees. 

.3 

LOGARITHMIC    TANGENTS, 


i 

Tangent  of  89  Degrees. 

P.  Part 

H 

0" 

10"         20" 

30" 

40" 

50" 

tol". 

0 

11.758079 

11.759287 

II  .760498 

ii  .761714 

II  .762932 

n.764i54 

59 

121.7 

i 

765379 

766608 

767840 

769076 

77o3i5 

77i558 

58 

123.8 

2 

772805 

774o55 

7753o8 

776566 

777826 

779°9I 

57 

125.9 

3 

780359 

78i63i 

782907 

784186 

785470 

786757 

56 

128.1 

4 

788047 

789342 

•790641 

791943 

79325o 

79456o 

55 

i3o.4 

5 

79^874 

797192 

7985i5 

799841 

801171 

8o25o6 

54 

132.8 

6 

8o3844 

805187 

8o6534 

807885 

809240 

810600 

53 

x55.3 

7 

811964 

8i3332 

814704 

816081 

817462 

8i8847 

52 

137-9 

8 

820237 

821632 

823o3i 

824434 

825842 

827255 

5i 

i4o.6 

9 

828672 

830094 

83i52o 

832951 

834387 

835828 

5o 

i43.4 

10 

11.837273 

11.838724 

11.840179 

ii.84i639 

n.843io4 

n.844574 

49 

146.2 

II 

846o48 

84?528 

849013 

85o5o3 

85i999 

853499 

48 

i49.3 

12 

855oo4 

8565i5 

858o3i 

859553 

861079 

862611 

47 

i52.4 

i3 

864149 

865692 

867240 

868794 

870354 

871919 

46 

i55.7 

i4 

873490 

875067 

876649 

878237 

879831 

88i43i 

45 

i59.i 

i5 

883o37 

884648 

886266 

887890 

889519 

891155 

44 

162.7 

16 

892797 

894446 

896100 

897761 

899429 

901103 

43 

166.4 

17 

902783 

904470 

906163 

907863 

909569 

911283 

42 

170.3 

18 
'9 

9i3oo3 
923469 

914730 
925239 

916464 
927015 

918205 
928799 

9i9953 
930590 

921707 
932388 

4i 
4o 

174.4 
178.7 

20 

11.934194 

11.936008 

ii  .937829 

11.939658 

11.941494 

H.943338 

39 

i83.3 

21 

945191 

94?o5  i 

948919 

950795 

952679 

954572 

38 

188.0 

22 

956473 

958382 

960299 

962225 

964160 

966103 

37 

193.0 

23 

968o55 

970016 

97i986 

973965 

975952 

977949 

36 

198.3 

24 

979956 

981971 

983996 

986o3o 

988074 

990128 

35 

203.9 

25 

992191 

994264 

996347 

99844o 

I2.ooo543 

12.002657 

34 

209.8 

26 

12.004781 

12.006915 

12.009060 

I2.OII2l5 

oi3382 

oi5559 

33 

216.2 

27 

017747 

019946 

O22l56 

024378 

026611 

028855 

32 

222.7 

28 

o3mi 

033379 

o35659 

o3795i 

o4o255 

042672 

3i 

229.8 

29 

044900 

047242 

049596 

o5i963 

o54342 

o56735 

3o 

237.3 

3o 

12.059142 

I2.o6i56i 

12.063994 

12.066441 

12.068902 

I2.07l377 

29 

245.4 

3i 

o73866 

076369 

078887 

o8i4i9 

083966 

o86529 

28 

254.O 

32 

089106 

091699 

094308 

o96932 

099572 

102228 

27 

263.2 

33 

104901 

107590 

110296 

n3oi9 

115760 

n85i7 

26 

273.2 

34 

121292 

I24o85 

126896 

129726 

132574 

i  3544o 

25 

283.9 

35 

138326 

I4l23l 

i44i56 

147100 

i5oo65 

i53o5o 

24 

295.4 

36 

i56o56 

159082 

i62i3o 

i65i99 

168290 

I7i4o4 

23 

3o8.o 

37 

i7454o 

177698 

180880 

i84o85 

i873i4 

I9o567 

22 

321.7 

38 

193845 

197148 

200476 

2o383o 

207210 

210616 

21 

336.7 

39 

2i4o49 

217510 

220998 

2245i5 

228060 

23i635 

2O 

353.1 

4o 

12.235239 

I2.238873 

12.242538 

12.246235 

12.249963 

I2.253723 

'9 

371.2 

4i 

257516 

261342 

2652o3 

269098 

273028 

276995 

18 

391.3 

42 

280997 

285o37 

289115 

293232 

297388 

3oi584 

17 

4i3.6 

43 

3o582i 

Sioioo 

3i4422 

318787 

323196 

32765o 

16 

438.7 

44 

332i5i 

336698 

341294 

345939 

35o634 

.  35538i 

i5 

467.0 

45 

36oi8o 

365o32 

369940 

374903 

379924 

385oo4 

i4 

499.2 

46 

390143 

395345 

400609 

4o5938 

4n333 

4i6796 

i3 

536.2 

4? 

422328 

427932 

4336io 

439362 

445192 

45noo 

12 

579«i 

48 

457091 

463i65 

469325 

475574 

481915 

488349 

II 

629.4 

49 

494880 

5oi5io 

5o8244 

5i5o83 

522032 

529094 

10 

689.4 

5o 

12.536273 

12.543572 

12.550996 

12.558549 

12.566236 

I2.574o6i 

9 

5i 

582o3o 

590148 

59842i 

6o6854 

6i5454 

624228 

8 

52 

633i83 

642327 

651667 

661212 

67O972 

68o956 

7 

53 

691175 

701641 

712365 

72336o 

73464i 

746223 

6 

54 

758122 

770357 

782946 

795911 

8o9275 

823o63 

5 

55 

8373o4 

852O27 

867267 

,  883o6i 

899452 

9  i  6485 

4 

56 

934214 

952697 

972002 

992208 

i3.oi3395 

i3.o3567i 

3 

57 

i3.o59i53 

13.083976 

i3.no3o5 

i3.  138334 

i68297 

200482 

2 

58 

235244 

273032 

3i4425 

36oi83 

4n335 

469327 

I 

59 

536274 

6i5455 

712365 

8373o4 

i4.oi3395 

i4.3i4425 

0 

60" 

50" 

40" 

30" 

90" 

10" 

c 

Co-tangent  of  0  Degree. 

i 

1  16 


NATURAL    SINES. 


.5 

X 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

o 

oooooo 

017452 

034899 

o52336  069756 

o87i56 

104528 

121869 

i39I73 

i56434 

60 

I 

0291 

7743 

5190 

2626 

070047 

7446 

48i8 

2i58 

946i 

6722 

59 

2 

o582 

8o34 

548  1 

2917 

o337 

7735 

5107 

2447 

9749 

7009  58 

3 

0873 

8325 

5772 

3207 

0627 

8025 

5396 

2735 

140037 

7296  57 

4 

1164 

8€i6 

6062 

3498 

0917 

83i5 

5686 

3024 

o325 

7584 

56 

5 

1454 

8907 

6353 

3788 

1207 

86o5 

5975 

33i3 

o6i3 

7871 

55 

6 

1745 

9197 

6644 

4079 

1497 

8894 

6264 

36oi 

0901 

8i58 

54 

7 

ao36 

9488 

6934 

4369 

1788 

9184 

6553 

3890 

1189 

8445 

53 

8 

2327 

9779 

7225 

466o 

2078 

9474 

6843 

4i79 

1477 

8732 

52 

9 

2618 

020070 

?5i6 

495o 

2368 

9763 

7132 

4467 

1765 

9020 

5i 

10 

002909 

O2o36i 

037806 

o5524i 

072658 

ogooSS 

107421 

124756 

i42o53 

159307 

5o 

ii 

32OO 

o652 

8097 

553i 

2948 

o343 

7710 

5o45 

234l 

9594 

49 

12 

3491 

0942 

8388 

5822 

3238 

o633 

7999 

5333 

2629 

9881 

48 

i3 

3782 

1233 

8678 

6112 

3528 

0922 

8289 

5622 

2917 

160168 

47 

i4 

4072 

i5a4 

8969 

6402 

38i8 

1212 

8578 

59io 

32o5 

o455 

46 

i5 

4363 

i8i5 

9260 

6693 

4io8 

i5o2 

8867 

6199 

3493 

o743 

45 

16 

4654 

2106 

955o 

6983 

4399 

1791 

9i56 

6488 

378o 

io3o 

44 

17 

4945 

2397 

984i 

7274 

4689 

2081 

9445 

6776 

4o68 

i3i7 

43 

18 

5236 

2687 

o4oi32 

7564 

4979 

2371 

9734 

7o65 

4356 

1604 

42 

'9 

5527 

2978 

0422 

7854 

5269 

2660 

IIOO23 

7353 

4644 

1891 

4i 

20 

oo58i8 

023269 

040713 

o58i45 

o75559 

092950 

Iio3i3 

127642 

144932 

162178 

4o 

21 

6109 

356o 

1004 

8435 

584n 

3239 

0602 

793o 

5220 

a465 

39 

22 

6399 

385i 

1294 

8726 

6i3<, 

3529 

0891 

8219 

55o7 

2752 

38 

23 

6690 

4i4i 

i585 

9016 

6429 

38i9 

1180 

85o7 

5795 

3o39 

37 

24 

6981 

4432 

1876 

93o6 

6719 

4io8 

1469 

8796 

6o83 

3326 

36 

25 

7272 

4723 

2166 

9597 

7009 

4398 

i758 

9o84 

637i 

36i3 

35 

26 

7563 

5oi4 

•2457 

9887 

7299 

4687 

2047 

9373 

6659 

3900 

34 

27 

7854 

53o5 

2748 

060177 

7589 

4977 

2336 

9661 

6946 

4i87 

33 

28 

8i45 

5595 

3o38 

o468 

7879 

5267 

2625 

9949 

7334 

44?4 

32 

29 

8436 

5886 

3329 

0758 

8169 

5556 

2914 

i3o238 

7522 

4761 

3i 

3o 

008727 

026177 

043619 

o6io49 

078459 

095846 

u32o3 

i3o526 

147809 

i65o48 

3o 

3i 

9017 

6468 

3910 

i339 

8749 

6i35 

3492 

o8i5 

8097 

5334 

29 

32 

93o8 

6759 

4201 

1629, 

9o39 

6425 

3781 

no3 

8385 

562i 

28 

33 

9599 

7049 

449i 

1920 

9329 

67i4 

4070 

i39i 

8672 

5908 

27 

34 

9890 

734o 

4782 

22IO 

96l9 

7004 

4359 

1680 

8960 

6i95 

26 

35 

010181 

763i 

5073 

25oo 

99°9 

7293 

4648 

1968 

9248 

648a 

25 

36 

0472 

7922 

5363 

2791 

o8oi99 

7583 

4937 

2256 

9535 

6769 

24 

3? 

o763 

8212 

5654 

3o8i 

o489 

7872 

5226 

2545 

9823 

7o56 

23 

38 

io54 

85o3 

5944 

337i 

07  79 

8162 

55i5 

2833 

i5om 

7342 

22 

39 

1  344 

8794 

6235 

366i 

io69 

845  1 

58o4 

3l2I 

o398 

762-; 

21 

4o 

oii635 

029085 

o46525 

063952 

081359 

098741 

n6o93 

i334io 

i5o686 

167916 

2O 

4i 

1926 

9375 

6816 

4242 

1649 

9o3o 

6382 

3698 

o973 

82o3 

*9 

42 

2217 

9666 

7106 

453s 

1939 

9320 

6671 

3986 

1261 

8489 

18 

43 

25o8 

9957 

7397 

4823 

2228 

96o9 

6960 

4274 

1  548 

8776 

«7 

44 

2799 

o3o248 

7688 

5n3 

25i8 

9899 

7249 

4563 

i836 

9o63 

16 

45 

3090 

0539 

7978 

54c3 

2808 

100188 

7537 

485i 

2123 

935o 

i5 

46 

338o 

0829 

8269 

5693 

3098 

o477 

7826 

5i39 

2411 

9636 

i4 

4? 

367i 

1120 

8559 

5984 

3388 

0767 

8n5 

5427 

2698 

9923 

i3 

48 

3962 

i4n 

885o 

6274 

3678 

io56 

84o4 

57i6 

2986 

170209 

12 

49 

4253 

1702 

9140 

6564 

3968 

1  346 

8693 

6oo4 

3273 

o496 

II 

5o 

oi4544 

031992 

o4943i 

o66854 

o84258 

ioi635 

118982 

136292 

i5356i 

170783 

10 

5i 

4835 

2283 

9721 

7i45 

4547 

1924 

9270 

658o 

3848 

1069 

9 

52 

5i26 

2574 

o5ooi2 

7435 

4837 

22l4 

9559 

6868 

4i36 

i356 

8 

53 

54i6 

2864 

0302 

7725 

5127 

25o3 

9848 

7i56 

4423 

i643 

7 

54 

57o7 

3i55 

oSgS 

8oi5 

54i7 

2793 

120137 

7445 

4710 

1929 

6 

55 

5998 

3446 

o883 

83o6 

5707 

3082 

0426 

7733 

4998 

2216 

5 

56 

6289 

3737 

H74 

8596   5997 

337I 

0714 

8021 

5285 

a5o2 

4. 

57 

658o 

4027 

1  464 

8886   6286 

366i 

ioo3 

83o9 

5572 

3789 

3 

58 

6871 

43i8 

i755 

91761   6576 

395o 

1292 

8597 

586o 

8075 

a 

59 

7162 

4609 

2o45 

9466J   6866 

4239 

i58i 

8885 

6147 

3362 

i 

89° 

88° 

87° 

86°   85° 

84° 

83° 

82° 

81° 

80° 

fl 

Natural  Co-sines. 

ifl 

S 

P.  P.  ,  ., 

tol»>85 

4.85 

4.84 

4.84 

4.83 

4.83 

4.82 

4.8i 

4.8o 

4.78 

NATURAL    TANGENTS. 


117 


1 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

o 

oooooo 

017455 

034921 

o524o8 

o69927 

087480. 

io5io4 

122785 

i4o54i 

i58384 

60 

I 

0291 

7746 

5212 

2699 

O7O2I9 

7782 

5398 

3o8o 

o837 

8683 

59 

2 

o582 

8037 

55o3 

299I 

o5u 

8o75 

5692 

3375 

n34 

898i 

58 

3 

o8y3 

8328 

5795 

3283 

0804 

8368 

5987 

367o 

i43i 

9279 

57 

4 

n64 

8619 

6086 

3575 

io96 

8661 

6281 

3966 

1728 

9577 

56 

5 

i454 

8910 

6377 

3866 

i389 

8954 

6575 

4261 

2024 

9876 

55 

6 

1745 

9201 

6668 

4i58 

1681 

9248 

6869 

4557 

2321 

160174 

54 

7 

2o36 

9492 

6960 

445o 

I973 

954i 

7i63 

4852 

2618 

0472 

53 

8 

2327 

9783 

725l 

4742 

2266 

9834 

7458 

5:47 

29l5 

0771 

52 

9 

2618 

020074 

7542 

5o33 

2558 

O9OI27 

7752 

5443 

3212 

iofi9 

5i 

10 

002909 

020365 

o37834 

o")5325 

072851 

O9o42I 

io8o46 

i25738 

i435o8 

i6i368 

5o 

ii 

32OO 

o656 

8i25 

56i7 

3i43 

07l4 

834o 

6o34 

38o5 

1666 

49 

12 

3491 

0947 

84i6 

59o9 

3435 

IOO7 

8635 

6329 

4lO2 

i965 

48 

i3 

3782 

1238 

8707 

6200 

3728 

i3oo 

8929 

6625 

4399 

2263 

47 

i4 

4072 

l529 

8999 

6492 

4O2O 

i594 

9223 

692O 

4696 

2562 

46 

i5 

4363 

1820 

9290 

6784 

43i3 

1887 

95i8 

7216 

4993 

2860 

45 

16 

4654 

2III 

958i 

7076 

46o5 

2180 

98l2 

75i2 

529o 

3i59 

44 

I? 

4945 

24O2 

9873 

7368 

4898 

2474 

110107!   7807 

5587 

3458 

43 

18 

5236 

2693 

o4oi64 

7660 

5i9o 

2767 

o4oil   8io3 

5884 

3756 

42 

J9 

552? 

2984 

o456 

795i 

,  5483 

3o6i 

o695 

8399 

6181 

4o55 

4i 

20 

oo58i8 

O23275 

040747 

o58243 

075775 

o93354 

no99o 

i28694 

146478 

164354 

4o 

21 

6109 

3566 

io38 

8535 

6068 

3647 

1284 

899o 

6776 

4652 

39 

22 

64oo 

3857 

i33o 

8827 

636i 

394i 

i579 

9286 

7o73 

495i 

38 

23 

6691 

4i48 

1621 

9u9 

6653 

4234 

i873 

9582 

737o 

525o 

37 

24 

6981 

4439 

1912 

94n 

6946 

4528 

2168 

9877 

7667 

5549 

36 

25 

7272 

473i 

2204 

97°3 

7238 

4821 

2463 

130173 

7964 

5848 

35 

26 

7563 

5022 

2495 

9995 

753i 

5n5 

2757 

o469 

8262 

6147 

34 

27 

7«54 

53i3 

2787 

060287 

7824 

54o8 

3o52 

0765 

8559 

6446 

33 

28 

8i45 

56o4 

3078 

o579 

8116 

5702 

3346 

1061 

8856 

6745 

32 

29 

8436 

5895 

3370 

0871 

84o9 

5995 

364i 

i357 

9i54 

7044 

3i 

3o 

008727 

026186 

o4366i 

061  i63 

078702 

o96289 

n3936 

i3i652 

i4945i 

167343 

3o 

3i 

9018 

6477 

3952 

i455 

8994 

6583 

4230 

i948 

9748 

7642 

29 

32 

9309 

6768 

4244 

1747 

9287 

6876 

4525 

2244 

i5oo46 

794i 

28 

33 

9600 

7o59 

4535 

2o39 

958o 

7170 

4820 

254o 

o343 

8240 

27 

34 

9891 

735o 

4827,   233i 

9873 

7464 

5n4 

2836 

o64i 

8539 

26 

35 

010181 

764i 

5n8:   2623 

o8oi65 

7757 

54o9 

3i32 

o938 

8838 

25 

36 

0472 

7933|   54io 

29l5 

o458 

8o5i 

5704 

3428 

1236 

9i37 

24 

3? 

o763 

8224'   5701 

3207 

0751 

8345 

5999 

3725 

i533 

9437 

23 

38 

io54 

85i5 

5993 

3499 

io44 

8638 

6294 

4021 

i83i 

9736 

22 

39 

1  345 

8806 

6284 

379i 

i336 

8932 

6588 

43i7 

2I29 

170035 

21 

4o 

on636 

029097 

o46576 

o64o83 

o8i629 

099226 

n6883 

i346i3 

152426 

I7o334 

20 

4i 

1927 

9388 

6867 

4375 

I922 

95i9 

7178 

49o9 

2724 

o634 

*9 

42 

2218 

9679 

7i59 

4667 

22l5 

98i3 

7473 

52o5 

3022 

o933 

18 

43 

2509 

997° 

745o 

4959 

25o8 

100107 

7768 

55o2 

33i9 

1233 

*7 

44 

2800 

O3O262 

77^2 

525i 

2801 

o4oi 

8o63 

5798 

36i7 

i532 

16 

45 

3091 

o553 

8o33 

5543 

3o94 

o695 

8358 

6o94 

39i5 

i83i 

i5 

46 

3382 

o844 

8325 

5836 

3386 

o989 

8653 

639o 

42l3 

2l3l 

i4 

4? 

3673 

n35 

8617 

6128 

3679 

1282 

8948 

6687 

45io 

243o 

i3 

48 

3964 

1426 

89o8 

6420 

3972 

1576 

9243 

6983 

48o8 

2730 

12 

49 

4254 

1717 

9200 

6712 

4265 

1870 

9538 

7279 

5io6 

3o3o 

II 

5o 

oi4545 

032009 

o4949i  067004 

o84558 

102164 

n9833 

i37576 

i554o4 

I?3329 

IO 

5i 

4836 

23oo 

9783   7296 

485  1 

2458 

120128 

7872 

5702 

3629 

9 

52 

5127 

259i 

o5oo75   ?589 

5i44 

2752 

o423 

8i69 

6000 

3929 

8 

53 

54i8 

2882 

o366   7881 

5437 

3o46 

0718 

8465 

6298 

4228 

7 

54 

57o9 

3I73 

o658   8173 

5730 

334o 

ioi3 

8761 

6596 

4528 

6 

55 

6000 

3465 

o949   8465 

6o23 

3634 

i3o8 

9o58 

6894 

4828 

5 

56 

6291 

3756 

1241   8758 

63i6 

3928 

1604 

9354 

7I92 

5127 

4 

57 

6582 

4o47 

i533   9o5o 

66o9 

4222 

i899 

965i 

749o 

5427 

3 

58 

6873 

4338 

1824 

9342 

69O2 

45i6 

2I94 

9948 

7788 

5727 

2 

59 

7164 

463o 

2116 

9635 

7i96 

48io 

2489 

i  40244 

8086 

6027 

I 

89° 

88° 

87° 

86° 

85° 

84° 

83° 

82°   81°  ' 

80° 

Natural  Co-tangents. 

* 

to  r'>85 

4.85 

4.86 

4.87 

4.88 

4-89 

4.9i 

4-93 

4-96 

4.98 

lib 


NATURAL    SINES. 


i 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

o 

i73648 

190809 

2079I2 

22495l 

24l922 

2588i9 

275637 

292872 

3o9oi7 

325568 

60 

i 

3935 

1095 

8196 

5234 

2204 

9ioo 

59i7 

265o 

9294 

5843 

59 

2 

4221 

i38o 

848  1 

55i8 

2486 

938i 

6i97 

2928 

957° 

6118 

58 

3 

45o8 

1666 

8765 

58oi 

2769 

9662 

6476 

3206 

9847 

6393 

57 

4 

4794 

I95i 

9o5o 

6o85 

3o5i 

9943 

6756 

3484 

3ioi23 

6668 

56 

'5,   5o8o 

2237 

9334 

6368 

3333 

260224 

7o35 

3762 

o4oo 

6943 

55 

6   5367 

2522 

96l9 

665  1 

36i5 

o5o5 

73i5i   4o4o 

0676 

7218 

54 

7 

5653 

2807 

99°3 

6935 

3897 

o785 

7594   43i8 

o953 

7493 

53 

8 

5^39 

3o93 

210187 

7218 

4i79 

1066 

7874 

4596 

I229 

7768 

52 

9 

6226 

3378 

0472 

75oi 

446i 

1  347 

8i53 

4874 

i5o6 

8042 

5i 

10 

176512 

i93664 

210756 

227784 

s44743 

261628 

278432 

295l52 

311782 

3283i7 

5o 

ii 

6798 

3949 

io4o 

8068 

0025 

I9o8 

8712 

543o 

2o59 

8592 

49 

12 

7o85 

4234 

13-25 

835i 

53o7 

2i89 

899i 

57o8 

2335 

8867 

48 

i3 

737i 

452o 

i6o9 

8634 

5589 

2470 

927° 

5986 

2611 

9i4i 

4? 

i4 

7657 

48o5 

i893 

8917 

587i 

2751 

955o 

6264 

2888 

94i6 

46 

i5 

7044 

5090 

2178 

9200 

6i53 

3o3i 

9829 

6542 

3i64 

969i 

45 

16 

823o 

5376 

2462 

9484 

6435 

33i2 

280108 

68i9 

344o 

9965 

44 

'7 

85i6 

566i 

2746 

9767 

6717 

3592 

o388 

7097 

37i6 

33o24o 

43 

18 

8802 

5946 

3o3o 

23oo5o 

6999 

3873 

0667 

7375 

3992 

o5i4 

42 

*9 

9088 

623i 

33i5 

o333 

7281 

4i54 

o946 

7653 

4269 

0-789 

4i 

20 

179375 

I965i7 

2i3599 

23o6i6 

247563 

264434 

281225 

29793o 

3i4545 

33io63 

4o 

21 

9661 

6802 

3883 

0899 

7845 

47i5 

i5o4 

8208 

4821 

i338 

39 

22 

9947 

7087 

4i67 

1182 

8126 

4995 

i783 

8486 

5o97 

1612 

38 

23 

i8o233 

7372 

445  1 

i465 

84o8 

5276 

2062 

8763 

5373 

i887 

37 

24 

0519 

7657 

4735 

1748 

869o 

5556 

234l 

_9o4i 

5649 

2161 

36 

25 

o8o5 

7942 

5oi9 

2031 

8972 

5~837 

2620 

93i8 

5925 

2435 

35 

26 

1091 

8228 

53o3 

23i4 

9253 

61  17 

2900 

9596 

6201 

27IO 

34 

27 

i377 

85i3 

5588 

2597 

9535 

6397 

3i79 

9873 

6477 

2984 

33 

28 

i663 

8798 

5872 

2880 

98i7 

6678 

3457 

3ooi5i 

6753 

3258 

32 

29 

1950 

9o83 

6i56 

3i63 

25oo98 

6958 

3736 

0428 

7O29 

3533 

3i 

3o 

182236 

I99368 

216440 

233445 

25o38o 

267238 

28401  5 

800706 

3n73o5 

3338o7 

3o 

3i 

2522 

9653 

6724 

3728 

0662 

75i9 

4294 

0983 

758o 

4o8i 

29 

32 

2808 

9938 

7008 

4oi  i 

o943 

7799 

4573 

1261 

7856 

4355 

28 

33 

3094 

20O223 

7292 

4294 

1225 

8o79 

4852 

i538 

8i32 

4629 

27 

34 

3379 

o5o8 

7575 

4577 

i5o6 

8359 

5i3i 

i8i5 

84o8 

4903 

26 

35 

3665 

o793 

7859 

4859 

1788 

864o 

54io 

2093 

8684 

5i78 

25 

36 

395i 

1078 

8i43 

5i42 

2o69 

8920 

5688 

2870 

8959 

5452 

24 

3? 

4237 

1  363 

8427 

5425 

235i 

92OO 

5967 

2647 

9235 

5726 

23 

38 

4523 

1  648 

8711 

5708 

2632 

•948o 

6246 

2924 

95u 

6000 

22 

39 

4809 

i933 

8995 

5990 

29l4 

9760 

6525 

3202 

9786 

6274 

21 

4o 

185095 

202218 

2I9279 

236273 

253i95 

270040 

286803 

3o3479 

320062 

336547 

2O 

4i 

538i 

2502 

9562 

6556 

3477 

0320 

•7082 

3756 

o337 

6821 

J9 

42 

5667 

2787 

9846 

6838 

3758 

0600 

736i 

4o33 

o6i3 

7o95 

18 

43 

5952 

3072 

22Ol3o 

7121 

4o39 

0880 

7639 

43io 

0889 

7369 

'7 

44 

6238 

3357 

o4i4 

?4o3 

4321 

1160 

79i8 

45'S7 

1  1  64 

7643 

16 

45 

6524 

3642 

o697 

7686 

4602 

i44o 

8i96 

4864 

i439 

79i7 

i5 

46 

6810 

3927 

o98i 

7968 

4883 

1720 

8475 

5i4i 

1715 

8i9o 

i4 

47 

7096 

4211 

1265 

«25l 

5i65 

2000 

8753 

54i8 

1990 

8464 

i3 

48 

738i 

4496 

1  548 

8533 

5446 

2280 

9o32 

5695 

2266 

8738 

12 

49 

7667 

478i 

i832 

8816 

5727 

256o 

93io 

5972 

254i 

9OI2 

II 

5o 

187953 

2o5o65 

222116 

239098 

256oo8 

272840 

289589 

3o6249 

322816 

339285 

IO 

5i 

8238 

535o 

2399 

938i 

6289 

3l20 

9867 

6526 

3092 

9559 

9 

52 

8524 

5635 

2683 

9663 

657i 

3400 

29oi45 

6So3 

3367 

9832 

8 

53 

8810 

592O 

2967 

9946 

6852 

3679 

0424 

7)8o 

3642 

34oio6 

7 

54 

9095 

6204 

325o 

240228 

7i33 

•3959 

O7O2 

?357 

39i7 

o38o 

6 

55 

938i 

6489 

3534 

o5io 

74i4 

4239 

o98i 

7633 

4i93 

o653 

5 

56 

9667 

6773 

3817 

o793 

7695 

45i9 

I259 

79io 

4468 

0927 

4 

57 

9952 

7o58 

4ioi 

1075 

7976 

4798 

i537 

8187   4743 

1200  3 

58 

190238 

?343 

4384 

i357 

8257 

5o78 

i8i5 

8464   5oi8 

i473  2 

59 

o523 

762-7 

4668 

i64o 

8538 

5358 

2094 

8740   5293   1747  i 

79° 

78° 

77° 

76° 

75°   74° 

73°  ;  72°   71°   70°   . 

1 

Natural  Co-sines. 

£#4.77  |  4.75 

4.73 

4.7i 

4.69 

4.67 

4.65 

4.62 

4.6o 

4.57 

NATURAL    TANGENTS. 


1  19 


J 

I 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

0 

i76327 

i9438o 

212667 

23o868 

249328 

267949 

286745 

3o573i 

324920 

344328 

60 

I 

6627 

4682 

2861 

1176 

9637 

8261 

7o6o 

6o4g 

6241 

4653 

69 

2 

6927 

4984 

3i65 

i48i 

9946 

8573 

7375 

6367 

5563 

4978 

58 

^ 

7227 

6286 

3469 

1788 

8885 

769o 

,  6685 

5885 

53o4 

57 

^ 

7627 

5588 

3773 

209^ 

066^ 

9197 

8oo5 

7oo3 

620-7 

563o 

56 

f 

7827 

6890 

4077 

2401 

0873 

8320 

7322 

6628 

5955 

55 

6 

8l27 

6192 

438i 

2707 

ii83 

9821 

8635 

764o 

685o 

6281 

54 

7 

8427 

6494 

4686 

3oi4 

1492 

270133 

895o 

•7969 

-71-72 

6607 

53 

8 

8727 

6796 

4990 

332i 

1801 

o445 

9266 

8277 

6933 

62 

9 

9028 

7099 

629^ 

3627 

2III 

0767 

958i 

8696 

7817 

7269 

5i 

10 

179328 

197401 

216699 

233934 

262420 

271069 

289896 

308914 

328139 

347585 

5o 

ii 

9628 

77°3 

59o3 

4241 

2729 

i382 

2902I  I 

9233 

846  1 

7911 

49 

12 

9928 

8oo5 

6208 

4548 

i6"94 

o527 

9662 

8783 

8237 

48 

i3 

180229 

83o8 

6612 

4855 

3348 

2006 

0842 

9871 

9106 

8563 

47 

i4 

0629 

8610 

6817 

6162 

3658 

2319 

1168 

310189 

9428 

8889 

46 

1  5 

0829 

8912 

7121 

5469 

3968 

263i 

i473 

0608 

9-761 

9216 

45 

16 

n3o 

9216 

7426 

6776 

4277 

2944 

1789 

082-7 

33oo73 

9642 

44 

1-7 

i43o 

9617 

773i 

6o83 

4587 

3256 

2106 

u46 

0396 

9868 

43 

18 

I73i 

9820 

8o35 

6390 

4897 

3569 

2420 

i465 

0-718 

360196 

42 

'19 

2031 

200122 

834o 

6697 

6207 

3882 

2736 

i784 

io4i 

0622 

4i 

20 

182332 

2OO425 

2x8645 

237004 

266616 

274194 

293o52 

3i2io4 

33i364 

35o848 

4o 

21 

2632 

0727 

8960 

7312 

6826 

4607 

3368 

2423 

1687 

1176 

39 

22 

2933 

io3o 

9264 

7619 

6i36 

4820 

3684 

2742 

2OIO 

1602 

38 

23 

3234 

i333 

9669 

7926 

6446 

5i33 

4ooo 

3o62 

2333 

1829 

37 

24 

3534 

i635 

9864 

8234 

6756 

5446 

43i6 

338i 

2666 

2166 

36 

25 

3835 

1938 

220169 

854i 

7o66 

6769 

4632 

37oo 

2979 

2483 

35 

26 

4i36 

224l 

0474 

8848 

7377 

6072 

4948 

4020 

3302 

2810 

34 

27 

4437 

2544 

0779 

9166 

7687 

6385 

6266 

4340 

3625 

3i37 

33 

28 

4737 

2847 

1084 

9464 

7997 

6698 

6681 

4669 

3949 

3464 

32 

29 

5o38 

3149 

i389 

9771 

83o7 

7011 

5897 

4979 

379i 

3i 

3o 

i85339 

203462 

221696 

268618 

277326 

296213. 

316299  334696 

354119 

3o 

3i 

564o 

3766 

2OOO 

o386 

8928 

7638 

653o 

6619 

49i9 

4446 

29 

32 

694  1 

4o58 

23o5 

o6g4 

9238 

7961 

6846 

5939 

6242 

4773 

28 

33 

6242 

436i 

2610 

1  002 

9549 

8266 

7i63 

6268 

5566 

5ioi 

27 

34 

6543 

4664 

2916 

i3io 

9869 

8678 

7480 

6578 

589o 

6429 

26 

35 

6844 

4967 

3221 

1618 

2601-70 

8891 

7796 

6899 

62i3 

6766 

25 

36 

7i45 

6271 

3526 

1926 

o48o 

9206 

8n3 

-7219'   6537 

6084 

24 

37 

7446 

5574 

3832 

2233 

o79i 

9619 

843o 

753g   6861 

6412 

23 

38 

7747 

5877 

4i37 

2641 

1  1  02 

9832 

8747 

•7869   -7186 

6740 

22 

39 

8o48 

6180 

4443 

2849 

i4i3 

280146 

9063 

81-79 

7^09 

7068 

21 

4o 

188349 

206483 

224748 

243167 

261-723 

280460 

299380 

3i85oo 

337833 

357396 

2O 

4i 

865i 

6787 

5o54 

3466 

2o34 

o773 

9697 

8820 

8167 

7724 

'9 

42 

8962 

7090 

536o 

3774 

2345 

1087 

3oooi4 

9i4i 

848  1 

8062 

18 

43 

9263 

7393 

5665 

4082 

2666 

i4oi 

o33i 

946i 

8806 

838o 

'7 

44 

9555 

7697 

6971 

4390 

2967 

1716 

0649 

9782 

9i3o 

8708 

16 

45 

9866 

8000 

6277 

4698 

3278 

2029 

0966 

32oio3 

9454 

9°37 

i5 

46 

190167 

83o4 

6583 

6007 

3589 

2343 

1283 

0423 

9779 

9365 

i4 

47 

0469 

8607 

6889 

53i5 

39oo 

2667 

1600 

o744 

34oio3 

9694 

i3 

48 

0760 

8911 

7194 

6624 

421  1 

2971 

1918 

1066 

0428 

360O22 

12 

49 

1062 

9214 

5932 

4523 

3286 

2235 

i386 

0762 

o35i 

II 

5o 

I9i363 

209618 

227806 

246241 

264834 

2836oo 

302553 

32I7O7 

341077 

360679 

IO 

5i 

1666 

9822 

8112 

6549 

5i45 

39i4 

28-70 

2028 

I4O2 

1008 

9 

52 

1966 

210126 

84i8 

6858 

5457 

4229 

3i88 

2349 

1727 

i337 

8 

53 

2268 

0429 

8724 

7166 

5768 

4543 

35o6 

26-70 

2062 

1666 

7 

54 

2670 

o733 

9o3i 

7476 

6o79 

4857 

3823 

2991 

2377 

1996 

6 

55 

2871 

1037 

9337 

7784 

639i 

5l72 

4i4i 

33i2 

2702 

2324 

5 

56 

3i73 

i34i 

9643 

8o92 

67O2 

5487 

4469 

3634 

3027 

2653 

4 

57 

3475 

1  645 

9949 

84oi 

7oi4 

6801 

4777 

3955 

3352 

2982 

3 

58 

3777 

1949 

230266 

8710 

7326 

6116 

6096 

4277 

3677 

33i2 

2 

59 

4078 

2253    0562 

9019 

7637 

643i 

54i3 

4698    4002 

364i 

I 

79° 

78°  !  77°   76° 

75°   74°   73° 

72°  !  71° 

70° 

a 

Natural  Co-tangents. 

i 

££*•« 

5.o5 

6.09 

5.i3 

5.i7 

5.22 

5.27 

5.33 

5.39 

5.46 

120 


NATURAL    SINES. 


J 

X 

20° 

21° 

22° 

23° 

24° 

25° 

26° 

27° 

28° 

29°  | 

o 

342020 

358368 

3746o7 

39073i 

4o6737 

422618 

43837i 

45399o 

469472 

484«  10 

60 

I 

2293 

864o 

4876 

°999 

7002 

2882 

8633 

425o 

9728 

5o64 

So 

2 

2567 

8911 

5i46 

1267 

7268 

3i45 

8894 

45o9 

9985 

53i8 

58 

3 

2840 

9i83 

54i6 

i534 

?534 

34o9 

9i55 

4768 

470242 

5573 

57 

4 

3n3 

9454 

5685 

1802 

7799 

3673 

94i7 

5027 

o499 

5827 

56 

5 

3387 

9725 

5955 

2070 

8o65 

3936 

9678 

5286 

o755 

6081 

55 

6 

366o 

9997 

6224 

2337 

833o 

4i99 

9939 

5545 

1012 

6335 

54 

7 

3933 

360268 

64g4 

26o5 

8596 

4463 

44O200 

58o4 

1268 

659o 

53 

8 

4206 

o54o 

6763 

2872 

8861 

4726 

0462 

6o63 

i525 

6844 

52 

9 

4479 

0811 

7o33 

3i4o 

9!27 

499o 

0723 

6322 

1-782 

7o98 

5i 

10 

344752 

361082 

3773o2 

3934o7 

4o9392 

425253 

44o984 

45658o 

472o38 

487352 

5o 

ii 

5o25 

i353 

757i 

3675 

9658 

55i6 

1245 

6839 

2294 

•7606 

49 

12 

5298 

i625 

784i 

3942 

9923 

5779 

i5o6 

•7098 

255i 

786o 

48 

i3 

557i 

1896 

8110 

4209 

4ioi88 

6042 

i767 

7357 

28o7 

8n4 

47 

i4 

5844 

2l67 

8379 

4477 

o454 

63o6 

2028 

76i5 

3o63 

8367 

46 

i5 

6117 

2438 

8649 

4744 

07i9 

6569 

2289 

7874 

3320 

8621 

45 

16 

6390 

2709 

8918 

5on 

o984 

6832 

255o 

8i33 

3576 

8875 

44 

I? 

6663 

2980 

9187 

5278 

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7o95 

2810 

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3832 

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43 

18 

6936 

325i 

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7358 

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7208 

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7621 

3332 

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4344 

9636 

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20 

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363793 

379994 

396o8o 

4i2o45 

427884 

443593 

459i66 

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21 

7754 

4o64 

380263 

6347 

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8i47 

3853 

9425 

4856 

49oi43 

39 

22 

8027 

4335 

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66i4 

2575 

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9683 

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38 

23 

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8935 

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1  664 

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28 

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1232   6647 

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2677 

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7042 

3221 

9283 

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28 

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7239 

2780'   8181;   3436 

26 

35 

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4027 

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25 

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448799  464327  4797i3 

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20 

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4842 

480223'  5459 

18 

43 

3747 

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2214 

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392I 

9579 

5ioo 

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6443 

2480 

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9839 

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7247 

3279 

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1499 

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466901 

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10 

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8320 

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6017 

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7i58 

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773i 

9 

52 

6194 

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6278 

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7416 

2773 

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8 

53 

6466 

2718 

8856 

4876 

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654o 

2175 

7673 

3o28 

8236 

7 

54 

6738 

2988 

9I24 

5:42 

io36 

6802 

2435 

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3282 

8488 

6 

55 

7010 

3258 

9392 

54o8 

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7o63 

2694 

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5 

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7281 

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7325 

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3792 

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4 

57 

7553 

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32i3 

8701 

4o46   9244 

3 

58 

7825 

4o67 

39oi96 

62o5 

209I 

7848 

3472 

8958 

43oi 

9496 

2 

59 

8096 

4337 

o463 

647i 

2355 

8110 

373r 

92l5 

/i  5  5  5 

9748 

I 

69° 

68° 

67° 

66° 

65° 

64° 

63° 

62° 

61°   60° 

d 

Natural  Co-sines. 

££4.54 

4.5i 

4-48 

4  45 

4.4i 

4.38 

4.34 

4.3o 

4.26 

4.23  ) 

NATLRAL    TANGENTS. 


121 


E 

20° 

21° 

22° 

23° 

24° 

25° 

26° 

27° 

28° 

29° 

0 

363970 

383864 

404026 

424475 

445229 

4663o8 

487733 

5o9525 

531709 

554309 

60 

I 

43oo 

4198 

4365 

48i8 

5577 

6662 

8o93 

9892 

2o83 

4689 

59 

2 

4629 

4532 

4703 

5i62 

5926 

7016 

8453 

5io258 

2456 

5070 

58 

3 

4959 

4866 

5o4a 

55o5 

6275 

737i 

88i3 

0625 

2829 

545o 

57 

4 

5288 

5200 

538o 

5849 

6624 

7725 

9174 

0992 

32o3 

583i 

56 

5 

56i8 

5534 

57i9 

6i92 

6973 

8080 

9534 

i359 

3577 

6212 

55 

6 

5948 

5868 

6o58 

6536 

7322 

8434 

9895 

I726 

3950 

6593 

54 

7 

6278 

6202 

6397 

6880 

767i 

8789 

490256 

2093 

4324 

6974 

53 

8 

6608 

6536 

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8020 

9i44 

0617 

2460 

4698 

7355 

52 

9 

6938 

687i 

7075 

7568 

8369 

9499 

0978 

2828 

5072 

7736 

5i 

10 

367268 

3872o5 

407414 

4279I2 

448-719 

469854 

491339 

5i3ig5 

535446 

558n8 

5o 

ii 

7598 

7540 

7753 

8256 

9d68 

47O209 

1700 

.  3563 

582i 

8499 

49 

12 

7928 

7874 

8092 

8601 

94i8 

o564 

2061 

3g3o 

6i95 

8881 

48 

i3 

8259 

8209 

8432 

8945 

9768 

0920 

2422 

4298 

657o 

9263 

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8589 

8544 

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9289 

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1275 

2784 

4666 

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3i45 

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73i9 

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45 

16 

9250 

9214 

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9979 

081-7 

1986 

35o7 

54o2 

7694 

0409 

44 

ll 

958i 

9549 

9-790 

43o323 

n67 

2342 

3869 

577o 

8o69 

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43 

18 

9911 

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4ioi3o 

0668 

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4  i  0810 

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23g3 

3269 

4478 

6042 

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37 

24 

1897 

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2739 

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4835 

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835i 

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347i 

36 

25 

2228 

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6767 

8720 

1074 

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35 

26 

2559 

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343o 

4322 

5548 

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9089 

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4238 

34 

27 

2890 

2903 

3192 

3775 

4673 

59o5 

7492 

9458 

1826 

4621 

33 

28 

3222 

3239 

3532 

4l2I 

5o24 

6262 

7855 

9828 

2203 

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32 

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29 

32 

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6429 

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28 

33 

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678i 

8047 

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4463 

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26 

35 

5543 

559a 

5919 

6543 

7484 

8762 

0399 

2417 

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769.4 

25 

36 

5875 

5928 

6260 

6889 

7836 

9120 

0763 

2787 

5218 

8079 

24 

37 

6207 

6265 

6601 

7236 

8188 

9477 

1  127 

3i58 

5595 

8464 

23 

38 

6539 

6601 

6943 

7582 

854o 

9835 

1491 

3528 

5973 

8849 

23 

39 

.  6872 

6938 

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7929!   8892  480193 

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3899 

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21 

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4i7626 

438276  459244!  48o55i 

502219 

524270 

546728 

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8622   9596   0909 

2583 

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7106 

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19 

42 

7869 

7948 

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8969!   9949 

1267 

2948 

5012 

7484 

0390 

18 

43 

8201 

8285 

865i 

9316  46o3oi 

1626 

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5383 

7862 

0776 

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44 

8534 

8622 

8993 

9663   o654 

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3677 

5754 

8240 

1161 

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8866 

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4o4i 

6i25 

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46 

9199 

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i359   27oi 

44o6 

6497 

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1933 

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47 

9532 

963/ 

4200I9 

0705 

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3o6o 

4771 

6868 

9876 

23ig 

i3 

48 

9864 

9971 

o36i 

io53|   2o65 

3419 

5i36 

7240 

9755 

2705 

12 

49 

380197 

o7oZ 

i4oo   2418 

3778 

55o2 

7612 

55oi34 

3092 

II 

5o 

38o53o 

4oo646 

421046 

441748  462771 

5o5867 

527984 

55o5i3 

5734-78 

IO 

5i 

o863 

0984 

i389 

2095!   3i24 

4496 

6232 

8356 

o892 

3865 

9 

5a 

1196 

1322 

I73i 

24^3   3478   4855 

6598 

8728 

1271 

4252 

8 

53 

i53o 

1660 

2074 

2791   383i 

52i4 

6963 

9100 

i65o 

4638 

7 

54 

i863 

1997 

24l7 

3i39   4i85 

5574 

7329 

9473 

2o3o 

5026 

6 

55 

2196 

2335 

2759 

3487   4538 

5933 

7695 

9845 

2409 

54i3 

5 

56 

253o 

2673 

3l02 

3835|   4892 

629; 

806 

53o2i8 

2789 

58oo 

4 

57 

2863 

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3445 

4i83|   5246 

6653 

8427 

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3169 

6187 

3 

58 

3i97 

335c 

3788 

4532J   56oo   7013 

8793 

0963 

3549 

6576 

2 

59 

353o 

3688 

4i3s 

488o   5g54   7373 

9i59 

1  336 

3929 

6962 

I 

69° 

68° 

67° 

66°   65°   64° 

63° 

62° 

61° 

60° 

s 

Natural  Co-tangenls. 

P.  P.  5  53 

5.6o 

5.68 

5.76 

5.85 

5.95 

6.o5 

6  16 

6.28 

I 

6.4o 

122 


NATURAL    SINES. 


1 
i 

30°   31° 

32° 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

0 

5ooooo|  5i5o38 

529919 

544639 

559i93 

573576 

587785 

6oi8i5 

6i566i 

629320 

60 

I 

0262 

5287 

53oi66 

4883 

9434 

38i5 

8021 

2o47 

589i 

9546:5q 

2 

o5o^ 

5537 

o4i3 

5l27 

9675 

4o53 

8256 

2280 

6120 

9772 

58 

i 

0756 

5786 

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537i 

99i6 

429I 

849i 

25l2 

6349 

9998  57 

^ 

1007 

6o35 

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56i5 

56oi57 

4529 

8726 

2744 

6578 

630224 

56 

| 

1259 

6284 

Il52 

5858 

o398 

4767 

896i 

2976 

68o7 

o45o 

55 

6 

i5n 

6533 

i399 

6102 

o639 

5oo5 

9i96 

3208 

7o36 

06-76 

54 

7 

1762 

6782 

1  645 

6346 

0880 

5243 

943i 

3440 

7265 

O9O2 

53 

8 

201^ 

7o3i 

1891 

6589 

II2I 

548  1 

9666 

3672 

7494 

1127 

52 

9 

2266 

7280 

2i38 

6833 

i36i 

57i9 

99oi 

39o4 

7722 

i353 

5i 

10 

5o25i7 

517529 

532384 

547076 

56i6o2 

575957 

59oi36 

6o4i36 

6i795i 

63i578 

5o 

ii 

2769 

7778 

263o 

7320 

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6i95 

0371 

4367 

8180 

1804 

49 

12 

3020 

8027 

2876 

7563 

2o83 

6432 

0606 

4599 

84o8 

2O29 

48 

r3 

3271 

8276 

3l22 

7807 

2324 

667o 

0840 

483i 

8637 

2255 

47 

i4 

3523 

8525 

3368 

8o5o 

2564 

69o8 

1075 

5o62 

8865 

2480 

46 

i5 

3774 

8773 

36i5 

8293 

28o5 

7i45 

i3io 

5294 

9094 

2705 

45 

16 

4oa5 

9022 

386i 

8536 

3o45 

7383 

1  544 

5526 

9322 

293l 

44 

i? 

4276 

9271 

4io6 

8780 

3286 

•7620 

i779 

' 

'  5757 

955i 

3i56 

43 

18 

4528 

95i9 

4352 

9O23 

3526 

785S 

20l3 

5988 

9779 

338i 

42 

J9 

4779 

9768 

4598 

9266 

3766 

8095 

2248 

6220 

62000-7 

36o6 

4i 

20 

5o5o3o 

520016 

534844 

5495o9 

564007 

578332 

592482 

6o645  i 

620235 

63383i 

4o 

21 

528i 

0265 

5ogo 

975a 

4247 

857o 

2716 

6682 

o464 

4o56 

39 

22 

5532 

o5i3 

5335 

9995 

4487 

88o7 

295i 

69i4 

0692 

4281 

38 

23 

5783 

0761 

558i 

55o238 

4727 

9o44 

3i85 

7i45 

0920 

45o6 

37 

24 

6o34 

1010 

5827 

o48i 

4967 

928l 

34i9 

7376 

n48 

473i 

36 

25 

6285 

1258 

6072 

0724 

5207 

95i8 

3653 

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i376 

4955 

35 

26 

6535 

i5o6 

63i8 

o966 

5447 

9755 

3887 

7838 

1604 

5i8o 

34 

27 

6786 

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6563 

1209 

5687 

9992 

4l2I 

8o69 

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33 

28 

7037 

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5927 

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2059 

5629 

32 

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6166 

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228-7 

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522499i  537300 

55i937 

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608-761 

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2747!    7545 

2180 

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2742 

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29 

32 

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2995!   779° 

2422 

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529o 

9223 

2970 

6527 

28 

33 

8290 

3242 

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2664 

7125 

i4i3 

5524 

9454 

3i97 

675i 

27 

34 

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3490 

8281 

2907 

7365 

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5758 

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26 

35 

8791 

3738 

8526 

3i49 

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1886 

599i 

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3652 

7200 

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3986 

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3392 

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2123 

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6ioi45 

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7424 

24 

37 

9292 

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3634 

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2359 

6458 

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4io7 

7648 

23 

38 

9542 

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9261 

3876 

8323 

2596 

6692 

0606 

4334 

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22 

39 

9792 

4729 

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2832 

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8096 

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5  ioo43 

524977 

53975i 

55436o 

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624-789 

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20 

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5224 

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540240 

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0-780 

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8438 

3i74 

7745 

2146 

6372 

O420 

4285 

7963 

i45o 

6 

55 

379i 

8685 

34i9 

7987 

2384 

6608 

o653 

45i5 

8189 

i673 

5 

56 

4o4o 

8932 

3663 

8228 

2623 

6844 

o885 

4744 

84i6 

1896 

4 

57 

4290 

9179 

39o7 

8469 

2861 

7°79 

1118 

4974 

8642 

2119 

3 

58 

4539 

9426   4i5r 

8710 

3  1  oo 

73i4 

i35o 

52o3 

8868 

2342 

2 

59 

4789 

9673!   4395 

8952 

3338 

755o 

1  58  3 

5432 

9o94 

2565 

I 

59° 

58°  !  57° 

56° 

55° 

54°   53° 

52°   51° 

50° 

0 

Natural  Co-sines. 

•9 

s 

P.P.  , 

to  I".4'18 

4.i3 

4.09 

4-o4 

4.oo 

3.95 

3.9o 

3.85  1  3.8o 

3.74 

NATURAL    TANGENTS. 


123 


d 

•  is 

30° 

31° 

32° 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

o 

SyySSo 

600861 

624869 

64g4o8 

6745o9 

700208 

726543 

753554 

781286 

809784 

60 

I 

7738 

1257 

5274 

9821 

4932 

o64i 

6987 

4oio 

1754 

810266 

59 

2 

8126 

i653 

5679 

650235 

5355 

1075 

7432 

4467 

2223 

o748 

58 

3 

85i4 

2049 

6o83 

0649 

5779 

i5o9 

7877 

4923 

2692 

1230 

57 

4 

89o3 

2445 

6488 

io63 

6203 

i943 

8322 

538o 

3i6i 

1712 

56 

5 

9291 

2842 

6894 

i477 

6627 

2377 

8767 

5837 

363i 

2195 

55 

6 

9680 

3239 

7299 

1892 

7o5i 

2812 

92l3 

6294 

4  1  00 

2678 

54 

7 

58oo68 

3635 

77°4 

23o6 

7475 

3246 

9658 

675i 

4570 

3i6i 

53 

8 

o457 

4o32 

8110 

272I 

79oo 

368i 

73oio4 

7209 

5o4o 

3644 

52 

9 

o846 

4429   85i6 

3i36 

8324 

4n6 

o55o 

7667 

55io 

4i~8 

5i 

10 

58i235 

604827 

628921' 

65355i 

678749 

7o455i 

73o996 

758i25 

785981 

8  i  46  i  2 

5o 

ii 

1625 

5224 

9327 

3966 

9i74 

4987 

i443 

8583 

645  1 

5o96 

49 

12 

2Ol4 

5622 

9734 

4382 

9599 

5422 

i889 

9o4i 

6922 

558o 

48 

i3 

24o3 

6019 

63oi4o 

4797 

680025 

5858 

2336 

95oo 

7394 

6o65 

47 

i4 

2793 

64i7 

o546 

52i3 

o45o 

6294 

2783 

9959 

7865 

6549 

46 

i5 

3i83 

68i5 

0953 

5629 

o876 

673o 

323o 

760418 

8336 

7034 

45 

16 

3573 

7213 

i36o 

6o45 

1302 

7i66 

3678 

0877 

8808 

75i9 

44 

J7 

3963 

7611 

I767 

646  1 

I728 

76o3 

4i25 

i336 

9280 

8oo5 

43 

18 

4353 

8010 

2174 

6877 

2i54 

8o39 

4573 

i796 

9752 

849i 

42 

X9 

4743 

84o8 

258i 

7294 

2680 

8476 

5021 

2256 

•790225 

8976 

4i 

20 

585i34 

608807 

632988 

657710 

683oo7 

7o89i3 

735469 

762716 

79°697 

8i9463 

4o 

21 

5524 

9205 

3396 

8127 

3433 

935o 

59i7 

3i76 

II70 

9949 

39 

22 

59i5 

9604 

38o4 

8544 

386o 

9788 

6366 

3636 

1  643 

820435 

38 

23 

63o6 

6iooo3 

421  1 

896i 

4287 

710225 

68i5 

4o97 

2II7 

O922 

37 

24 

6697 

o4o3 

4619 

9379 

47i4 

o663 

•7264 

4558 

2590 

i4o9 

36 

25 

7088 

0802 

5027 

9796 

5i42 

I  IOI 

77i3 

5oi9 

3o64 

i897 

35 

26 

74?9 

1201 

5436 

660214 

5569 

i539 

8162 

548o 

3538 

2384 

34 

27 

7870 

1601 

5844 

o63i 

5997 

i977 

8611 

594i 

4012 

2872 

33 

28 

8262 

2001 

6253 

io49 

6425 

2416 

9o6i 

64o3 

4486 

336o 

32 

29 

8653 

2401 

6661 

1467 

6853 

2854 

95n 

6865 

4961 

3848 

3i 

3o 

589045 

6l28oi 

637070 

661886 

68728i 

713293 

789961 

767827 

795436 

824336 

3o 

3i 

9437 

3201 

7479 

23o4 

77°9 

3732 

74o4i  i 

7789 

5911 

4825 

29 

32 

9829 

36oi 

7888 

2723 

8i38 

4171 

0862 

8252 

6386 

53x4 

28 

33 

590221 

.   4002 

8298 

3i4i 

8567 

46n 

l3l2 

87i4 

6862 

58o3 

27 

34 

o6i3 

4402 

8707 

356o 

8995 

5o5o 

i763 

9.177 

7337 

6292 

26 

35 

1006 

48o3 

9117 

3979 

9/125 

5490 

22l4 

964o 

78i3 

6782 

25 

36 

i398 

5204 

9527 

4398 

9854 

593o 

2666 

770104 

8290 

7272 

24 

3? 

1791 

56o5 

9937 

48i8 

690283 

637o 

3ii7 

0567 

8766 

7762 

23 

38 

2184 

6006 

640347 

5237 

o7i3 

6810 

3569 

io3i 

9242 

8252 

22 

39 

2577 

64o8 

o757 

5657 

n43 

725o 

4020 

i495 

9719 

8743 

21 

4o 

592970 

616809 

641167 

666o77 

69i572 

717691 

744472 

771959 

•800196 

829234 

2O 

4i 

3363 

7211 

i578 

6497 

2003 

8i32 

4925 

2423 

0674 

9725 

I9 

42 

3757 

76i3 

1989 

69i7 

2433 

8573 

5377 

2888 

n5i 

83o2i6 

18 

43 

4i5o 

8oi5 

2399 

7337 

2863 

9014 

583o 

3353 

1629 

o7o7 

17 

44 

4544 

84i7 

2810 

7758 

3294 

9455 

6282 

38i8 

2107 

n99 

16 

45 

4937 

8819 

3222 

8i79 

3725 

9897 

6735 

4283 

a585 

i69i 

i5 

46 

533i 

9221 

3633 

8599 

4i56 

720339 

7i89 

4748 

3o63 

2i83 

i4 

4? 

5725 

9624 

4o44 

9O2O 

4587 

0781 

•7642 

52i4 

3542 

2676 

i3 

48 

6iao 

620026 

4456 

9442 

5oi8 

1223 

8o96 

568o 

4O2I 

3i69 

12 

49 

65i4 

0429 

4868 

9863 

545o 

i665 

8549 

6i46 

45oo 

3662 

II 

5o 

596908 

620832 

64528o 

67o284 

69588r 

722108 

749oo3 

776612 

804979 

834i55 

10 

Si 

73o3 

1235 

5692 

o7o6 

63i3 

255o 

9458 

7078 

5458 

4648 

9 

62 

7698 

i638 

6io4 

1128 

6745 

2993 

99I2 

7545 

5938 

5i42 

8 

53 

8093 

2042 

65i6 

i55o 

7177 

3436 

75o366 

8012 

64i8 

5636 

7 

54 

8488 

2445 

6929 

I972 

7610 

3879 

0821 

8479 

6898 

6i3o 

6 

55 

8883 

2849 

7342 

2394 

8042 

4323 

I276 

8946 

7379 

6624 

5 

56 

9278 

3253 

7755 

2817 

8475 

4766 

i73i 

94i4 

7859 

7119 

4 

57 

9674 

3657 

8168 

324o 

89o8 

52IO 

2187 

9881 

834o 

76i4 

3 

58 

6ooo6c 

4o6i 

858i 

3662 

934i 

5654 

2642 

780349 

8821 

8io9 

2 

59 

o465 

4465 

8994 

4o85 

9774 

6o98 

3o98 

0817 

93o3 

86o4 

I 

59° 

58°  '  57° 

56° 

55° 

54° 

53° 

52° 

51° 

50° 

. 

Natural  Co-tangents. 

S 

tor'.6-53 

6.67 

6.82 

6.97 

7-i4 

7.3i 

7.5o 

7.70 

7.92 

8.:4 

124 


NATURAL    SINES. 


.B 

X 

40° 

41° 

42° 

43° 

44° 

453 

46° 

47° 

48° 

49° 

0 

642788 

656o59 

669i3i 

68i998 

694658 

707107 

7i934o 

73i354 

743i45 

7547io 

60 

I 

3oio 

6279 

9347 

2211 

4868 

7312 

9542 

i552 

3339 

49oo 

59 

r 

3233 

6498 

9563 

2424 

5o77 

75i8 

9744 

i75o 

3534 

5o9i 

58 

2 

3456 

6717 

9779 

2636 

5286 

7724 

9946 

i949 

3728 

5a82 

57 

4 

3679 

6937 

9995 

a849 

5495 

7929 

72oi48 

2l47 

3923 

5472 

56 

i 

3901 

7i56 

670211 

3o6i 

57o4 

8i34 

o349 

2345 

4n7 

5663 

55 

6 

4124 

7375 

0427 

3274 

5913 

834o 

o55i 

2543 

43i2 

5853 

54 

^ 

4346 

7594 

0642 

3486 

6122 

8545 

o753 

2741 

45o6 

6o44 

53 

8 

4569 

7814 

o858 

3698 

633o 

875o 

o954 

2939 

47oo 

6234 

52 

9 

4791 

8o33 

1074 

39n 

6539 

8956 

n56 

3i37 

4894 

6425 

5i 

10 

645oi3 

658252 

67i289 

684i23 

696748 

7o9i6i 

72i357 

733334 

745o88 

7566i5 

5o 

ii 

5236 

8471 

i5o5 

4335 

6957 

9366 

i559 

3532 

5282 

68o5 

49 

12 

5458 

8689 

1721 

4547 

7i65 

957i 

I76o 

373o 

5476 

6995 

48 

i3 

568o 

8908 

i936 

4759 

7374 

9776 

I962 

3927 

5670 

7i85 

47 

i4 

5902 

9127 

2l5l 

4971 

7582 

998i 

2i63 

4i25 

5864 

7375 

46 

i5 

6124 

9346 

2367 

5i83 

779° 

7ioi85 

2364 

4323 

6057 

7565 

45 

16 

6346 

9565 

2582 

5395 

7999 

o39o 

2565 

4520 

625i 

7755 

44 

17 

6568 

9783 

2797 

5607 

8207 

o595 

2766 

4717 

6445 

7945 

43 

18 

6790 

660002 

3oi3 

58i8 

84i5 

0799 

,2967 

49i5 

6638 

8i34 

42 

'9 

7012 

O22O 

3228 

6o3o 

8623 

ioo4 

3i68 

5lI2 

6832 

8324 

4i 

20 

64?233 

660439 

673443 

686242 

698832 

7II209 

723369 

7353o9 

747025 

7585i4 

4o 

21 

7455 

o657 

3658 

6453 

9o4o 

i4i3 

357o 

55o6 

7218 

87o3 

39 

22 

7677 

o875 

3873 

6665 

9248 

1617 

377i 

57o3 

7412 

8893 

38 

23 

7898 

1094 

4o88 

6876 

9455 

1822 

397i 

59oo 

76o5 

9o82 

37 

24 

8120 

I3l2 

43o2 

7088 

9663 

2026 

4l72 

6097 

7798 

927i 

36 

25 

834i 

i53o 

45i7 

7299 

9871 

2280 

4372 

6294 

799i 

946i 

35 

26 

8563 

1748 

4732 

75io 

700079 

2434 

4573 

649i 

8i84 

965o 

34 

27 

8784 

1966 

4947 

7721 

0287 

2639 

4773 

6687 

8377 

9839 

33 

28 

9006 

2184 

5i6i 

7932 

0494 

2843 

4974 

6884 

857o 

76oo28 

32 

29 

9227 

2402 

5376 

8i44 

0702 

3o47 

5i74 

7081 

8763 

02  I  7 

3i 

3o 

649448 

662620 

67559o 

688355 

700909 

7i325o 

725374 

737277 

748956 

76o4o6 

3o 

3i 

9669 

2838 

58o5 

8566 

1117 

3454 

5575 

7474 

9i48 

o595 

29 

32 

9890 

3o56 

60  1  9 

8776 

1  324 

3658 

5775 

7670 

934i 

o784 

28 

33 

65oiii 

3273 

6233 

8087 

i53i 

3862 

5975 

7867 

9534 

0972 

27 

34 

o332 

349i 

6448 

9198 

i739 

4o66 

6i75 

8o63 

9726 

1161 

26 

35 

o553 

37o9 

6662 

9409 

i946 

4269 

6375 

8259 

99i9 

i35o 

25 

36 

0774 

3926 

6876 

9620 

2i53 

4473 

6575 

8455 

75oin 

i538 

24 

3? 

o995 

4i44 

700.0 

983o 

236o 

4676 

6775 

865i 

o3o3 

I727 

23 

38 

1216 

436i 

73o4 

690041 

2567 

488o 

6974 

8848 

o496 

I9i5 

22 

39 

i437 

4579 

75i8 

O25l 

2774 

5o83 

7i74 

9o43 

0688 

2104 

21 

4o 
4i 

*Ai657 
1878 

664796 
5oi3 

677732 
7946 

690462  702981 
0672   3i88 

7i5286 
549o 

727374 
7573 

739a39 
9435 

75o88o 

I072 

762292 

2480 

20 
19 

42 

2098 

523o 

8160 

0882   3395 

5693 

7773 

963i 

1264 

2668 

18 

43 

2319 

5448 

8373 

1093 

36oi 

5896 

7972 

9827 

i456 

2856 

i? 

44 

z539 

5665 

8587 

i3o3 

38o8 

6o99 

8172 

74oo23 

1  648 

3o44 

16 

45 

2760 

5882 

8801 

i5i3 

4oi5 

6302 

837i 

0218 

1840 

3232 

i5 

46 

2980 

6099 

9oi4 

1723 

4221 

65o5 

857o 

o4i4 

2032 

3420 

i4 

4? 

3200 

63i6 

9228 

i933 

4428 

6708 

8769 

o6o9 

2223 

36o8 

i3 

48 

3421 

6532 

944i 

2i43 

4634 

69n 

8969 

o8o5 

24i5 

3796 

12 

49 

364i 

6749 

965$ 

2353 

484  1 

7113 

9i68 

IOOO 

2606 

3984 

II 

5o 

t»5386i 

666966 

679868 

692565 

7o5o47 

7'73i6 

729367 

74n95 

752798 

764i7i 

IO 

5i 

4o8i 

7i83 

680081 

2773 

5253 

75i9 

9566 

i39i 

2989 

4359 

9 

52 

43oi 

7399 

O295 

2983 

5459 

772i 

9765 

i586 

3i8i 

4547 

8 

53 

452i 

7616 

o5o8 

3192 

5665 

7924:  9963 

1781 

3372 

4734 

7 

54 

4?4i 

7833 

0721 

3402 

5872 

8i26)  73oi62 

1976 

3563 

492I 

6 

55 

4961 

8o49 

o934 

36n 

6078 

8329'   o36i 

2171 

3755 

5io9 

5 

56 

5i8o 

8265 

n47 

382i 

6284 

853i 

o56o 

2366 

3946 

5296 

4 

57 

54oo 

8482 

i36o 

4o3o 

6489 

8733 

o758 

256i 

4i37 

5483 

3 

58 

5620 

8698 

i573 

424o 

6695 

8936 

o957 

2755 

4328 

567o 

a 

J»9 

5839 

89i4 

1786 

4449   6901 

9i38 

n55 

295o 

45i9 

5857 

1  > 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42° 

41° 

40° 

c 

Natural  Co-sines. 

y 

P.  P.  ,  f 
tol".3'69 

3.63 

3.57 

3.52 

3.46 

3.4o 

3.34 

3.27 

3.21 

3.i5 

NATURAL    TANGENTS. 


125 


i 

_J 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

48° 

49° 

o 

839100 

869287 

9oo4o4,  9325i5 

965689 

I.OOOOO 

i.o3553 

1.07237 

i.  11061 

i.i5o37 

60 

I 

9595 

9798 

oq3il   3o59 

625i 

oo58 

36i3 

7299 

1126 

5io4 

59 

2 

840092 

870309 

i458 

36o3 

68:4 

0116 

3674 

7362 

i  i9i 

5172 

58 

3 

o588 

0820 

i985 

4i48 

7377 

oi75 

3734 

7425 

1256 

fo4o 

57 

4 

1084 

i332 

25i3 

4693 

79/.o 

oa33 

3794 

7487 

l32I 

53o8 

56 

5 

i58i 

i843 

3o4i 

5a38 

85o4 

0291 

3855 

755o 

1387 

5375 

55 

6 

2078 

2356 

3569 

5783 

9o67 

o35o 

39i5 

76i3 

i452 

5443 

54 

7 

2575 

2868 

4o98 

6329 

9632 

0408 

3976 

7676 

i5i7 

55  ii 

53 

8 

3o73 

338i 

4627 

6875 

97oi96 

o467 

4o36 

7738 

i582 

5579 

52 

9 

357i 

3894 

5x56 

7422 

o76i 

o525 

4o97 

7801 

1  648 

5647 

5i 

10 

844069 

874407 

9o5685 

937968 

97i326 

i.oo583 

I.o4i58 

1.07864 

1.11713 

i.  15716 

5o 

ii 

4567 

4920 

62i5 

85i5 

1892 

0642 

4218 

7927 

1778 

5783 

49 

12 

5o66 

5434 

6745 

9o63 

2458 

O7OI 

4279 

799° 

1  844 

585i 

48 

i3 

5564 

5948 

7275 

96io 

3o24 

°759 

434o 

8o53 

1909 

5919 

47 

i4 

6o63 

6462 

78o5 

94oi58 

3590 

0818 

44oi 

8116 

i975 

5987 

46 

i5 

656a 

69.76 

8336 

0706 

4i57 

o876 

446  1 

8179 

2041 

6o56 

45 

16 

7062 

749i 

8867 

1255 

4724 

0935 

4522 

8243 

2106 

6124 

44 

17 

7562 

8006 

9398 

i8o3 

5291 

0994 

4583 

83o6 

2172 

6192 

43 

18 

8062 

852i 

993o 

2352 

5859 

io53 

4644 

8369 

2238 

6261 

42 

*9 

8562 

9o37 

9io462 

29O2 

6427 

III2 

47o5 

8432 

23o3 

6329 

4i 

20 

849062 

879553 

9io994 

94345i 

976996 

I.OII7O 

i.o4766 

1.08496 

1.12369 

i.i6398 

4o 

21 

9563 

88oo69 

i526 

4ooi 

7564 

1229 

482-7 

855g 

2435 

6466 

39 

22 

85oo64 

o585 

2o59 

4552 

8i33 

1288 

4888 

8622 

25oi 

6535 

38 

23 

o565 

1102 

2592 

5l02 

87o3 

1  347 

4949 

8686 

2567 

66o3 

37 

24 

1067 

l6l9 

3i25 

5653 

9272 

i4o6 

5oio 

8749 

2633 

6672 

36 

25 

i568 

2i36 

3659 

6204 

9842 

i465 

5o72 

88i3 

2699 

6741 

35 

26 

2070 

2653 

4i93 

6756 

980413 

i524 

5i33 

8876 

2765 

6809 

34 

27 

2573 

3l?I 

4727 

73o7 

0983 

i583 

5i94 

8940 

283i 

6878 

33 

28 

3o75 

3689 

526i 

7859 

i554 

1  642 

5255 

9003 

2897 

6947 

32 

29 

3578 

4207 

5796 

8412 

2126 

1702 

53i7 

9067 

2963 

7016 

3i 

3o 

854o8i 

884725 

9i633i 

948g65 

98269*7 

1.01761 

1.06378 

1.09131 

1.13029 

1.17085 

3o 

3i 

4584 

5244 

.6866 

95!8 

3269 

1820 

5439 

9i95 

3096 

7i54 

99 

32 

5o87 

5763 

'7402 

950071 

3842 

1879 

55oi 

9258 

3i62 

7223 

•28 

33 

559i 

6282 

7938 

0624 

44i4 

1939 

5562 

9322 

3228 

7292 

27 

34 

6095 

6802 

8474 

1178 

4987 

1998 

5624 

9386 

3295 

736i 

26 

35 

6599 

7321 

9oio 

I733 

556o 

2057 

5685 

945o 

336i 

743o 

25 

36 

7104 

7842 

954? 

2287 

6i34 

2117 

5747 

95i4 

3428 

75oo 

24 

37 

7608 

8362 

920084 

2842 

67o8 

2176 

58o9 

9578 

3494 

7569 

23 

38 

8n3 

8882 

0621 

3397 

•7282 

2236 

587o 

9642 

356i 

7638 

22 

39 

8619 

94o3 

iiSg 

3953 

7857 

2295 

5932 

97o6 

3627 

7708 

21 

4o 

859124 

889924 

921697 

9545o8 

988432 

1.02355 

i.o5994 

i.o977o 

1.13694 

1.17777 

2O 

4i 

9630 

890446 

2235 

5o64 

9oo7 

24i4 

6o56 

9834 

376i 

7846 

J9 

42 

86oi36 

0967 

2773 

562i 

9582 

2474 

6117 

9899 

3828 

7916 

18 

43 

o64a 

i489 

33i2 

6177 

99oi58 

2533 

6179. 

o963 

3894 

7986 

ll 

44 

n48 

2OI2 

385i 

6734 

o735 

2593 

6241 

1.10027 

396i 

8o55 

16 

,43 

i655 

2534 

4390 

720.2 

i3n 

2653 

63o3 

oo9i 

4028 

8i25 

i5 

46 

2162 

3o57 

493o 

7849 

1888 

2713 

6365 

oi56 

4095 

8194 

i4 

4? 

2669 

358o 

5470 

84o7 

2465 

2772 

6427 

O22O 

4162 

8264 

i3 

48 

3i77 

4io3 

6010 

8966 

3o43 

2832 

6489 

0285 

4229 

8334 

12 

49 

3685 

4627 

655i 

9524 

362i 

280.2 

655i 

.  o349 

4296 

84o4 

II 

5o 

864i93 

895i5i 

927091 

96oo83 

994199 

I.O2952 

i.o66i3 

i.io4i4 

r.  14363 

i.i8474 

10 

5i 

4701 

5675 

7632 

0642 

4778 

3012 

6676 

0478 

443o 

8544 

9 

52 

5209 

6199 

8174 

I2O2 

5357 

3072 

6738 

o543 

4498 

86i4 

8 

53 

57i8 

6724 

87i5 

1761 

5936 

3i32 

6800 

0607 

4565 

8684 

7 

54 

6227 

7249   9257 

2322 

65i5 

3l92 

6862 

0672 

4632 

8754 

6 

55 

6736 

7774 

9800 

2882 

7°95 

3252 

6925 

o737 

4699 

8824 

5 

56 

7246 

8299 

93o342 

3443 

7676 

33i2 

6987 

0802 

4767 

8894 

4 

5? 

7756 

8825 

o885 

4oo4 

8256 

3372 

7049 

0867 

4834 

8964 

3 

58 

8266 

935i 

i4a8 

4565 

8837 

3433 

7112 

o93i 

4902 

9o35 

2 

59 

8776 

9877 

1971 

5127 

94i8 

3493 

7174 

o996 

4969 

9io5 

I 

49° 

48° 

47° 

46° 

45° 

44° 

43° 

42°    41° 

40°   . 

Natural  Co-tangents. 

*g 

P.  P«  Q   OQ 

tol".8"38 

8.64 

8.92 

9  21 

9.53 

0.99    1.02    I.  06 

i.  10   i.i5 

126 


NATURAL    SINES. 


A 

X 

50C 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

0 

766044 

777146 

788011 

798636 

809017 

819152 

829038 

83867i 

848o48 

857i67 

60 

I 

623i 

?329 

8190 

8811 

9188 

93i9 

9200 

8829 

8202 

73i7 

59 

2 

64x8 

7512 

8369 

8985 

9359 

9486 

9363 

8987 

8356 

7467 

58 

3 

66o5 

7695 

8548 

9160 

953o 

9662 

9525 

9i46 

85io 

•7616 

57 

4 

6792 

7878 

8727 

9335 

9700 

9819 

9688 

93o4 

8664 

7766 

56 

5 

6979 

8060 

8905 

95io 

9871 

9985 

985o 

9462 

8818 

79i5 

55 

6 

7i65 

8243 

9084 

9685 

810042 

820152 

83ooi2 

962O 

8.972 

8o65 

54 

7 

7352 

8426   9263 

9859 

O2I2 

o3i8 

0174 

9778 

9125 

8214 

53 

8 

7538 

8608;   9441 

8ooo34 

o383 

o485 

o337 

9936 

9279 

8364 

52 

9 

7725 

8791 

9620 

0208 

o553 

o65i 

o499 

84oo94 

9433 

85i3 

5i 

10 

767911 

778973 

789798 

8oo383 

810723 

820817 

83o66i 

84o25i 

849586 

858662 

5o 

ii 

8097 

9i56 

9977 

o557 

0894 

o983 

0823 

o4o9 

9739 

8811 

49 

12 

8284 

9338 

79Oi55 

0731 

1064 

n49 

o984 

o567 

9893 

896o 

48 

i3 

8470 

9520 

o333 

o9o6 

1234 

i3i5 

n46 

0724 

85oo46 

9io9 

47 

i4 

8656 

9702 

o5ii 

1080 

i4o4 

i48i 

i3o8 

0882 

oi99 

9258 

46 

i5 

8842 

9884 

0690 

1254 

i574 

i647 

i47o 

io39 

o352 

94o6 

45 

16 

9028 

780067 

0868 

1428 

1744 

i8i3 

i63i 

1  196 

o5o5 

9555 

44 

«7 

9214 

0249 

io46 

1602 

1914 

1978 

i793 

1  3  54 

o658 

97o4 

43 

18 

9400 

o43o 

1224 

1776 

2084 

2i44 

i954 

i5n 

0811 

9852 

42 

J9 

9585 

0612 

i4oi 

i949 

2253 

23lO 

2Il5 

1668 

o964 

860001 

4i 

20 

769771 

780794 

791579 

802123 

812423 

822475 

832277 

84i825 

85iu7 

86oi49 

4o 

21 

9957 

0976 

1757 

2297 

2592 

2641 

2438 

I982 

I269 

0297 

39 

22 

770142 

n57 

1935 

2470 

2762 

2806 

2599 

2l39 

1422 

o446 

38 

23 

o328 

i339 

21  12 

2644 

2g3i 

297I 

2760 

2296 

i575 

o594 

37 

24 

o5i3 

l520 

2290 

2817   3ioi 

3i36 

292I 

2452 

1727 

0742 

36 

25 

0699 

1702 

2467 

2991 

3270 

33o2 

3082 

26o9 

1879 

o89o 

35 

26 

o884 

i883 

2644 

3i64 

3439 

3467 

3243 

2766 

2032 

io38 

34 

27 

1069 

2o65 

2822 

3337 

36o8 

3632 

34o4 

2922 

2184 

1186 

33 

28 

1254 

2246 

2999 

35n 

3778 

3797 

3565 

3o79 

2336 

i334 

32 

29 

i44o 

2427 

3176 

3684 

3^7 

396i 

3725 

3235 

2488 

i48i 

3i 

3o 

771625 

782608 

793353 

8o3857 

8i4n6 

824126 

833886 

84339i 

85264o 

861620. 

3o 

3i 

1810 

2789 

353o 

4o3o 

4284 

429I 

4o46 

3548 

2792 

1777 

29 

32 

i995 

2970 

37o7 

4203 

4453 

4456 

4207 

37o4 

2944 

I924 

28 

33 

2179 

3i5i 

3884 

4376 

4622 

4620 

4367 

386o 

3o96 

2072 

27 

34 

2364 

3332 

4o6i 

4548 

4791 

4?85 

4527 

4oi6 

3248 

2219 

26 

35 

2549 

35i3 

4238 

4721 

4959 

4949 

4688 

4172 

3399 

2366 

25 

36 

2734 

3693 

44i5 

4894 

5i28 

5u3 

4848 

4328 

355i 

25i4 

24 

3? 

2918 

3874 

459i 

5o66 

5296 

5278 

5oo8 

4484 

3702 

2661  23 

38 

3io3 

4o55 

4768 

5239 

5465 

5442 

5i68 

464o 

3854 

28"- 

39 

3287 

.  4235 

4944 

'  54n 

5633 

56o6 

5328 

4795 

4oo5 

2955 

21 

4o 

773472 

784416 

795121 

8o5584 

8i58oi 

825770 

835488 

84495i 

854i56 

863io2 

2O 

4i 

3656 

4596 

5297 

6756 

5969 

5934 

5648 

5io6 

43o8 

3249  19 

42 

384o 

4776 

5473 

5928 

6i38 

6o98 

58o7 

5262 

4459 

3396  1  8 

43 

4024 

4957 

565o 

6100 

63o6 

6262 

5967 

54i7 

46io 

3542  17 

44 

4209 

5i37 

5826 

6273 

64?4 

6426 

6127 

5573 

4761 

36-Sy  1  6 

45 

4393 

53i7 

6002 

6445 

6642 

659o 

6286 

5728 

49I2 

3836  1  5 

46 

4577 

5497 

6178 

6617 

6809!   6753 

6446 

5883 

5o63 

3982  14 

4? 

4761 

5677 

6354 

6788 

6977!   6917 

66o5 

6o38 

52i4 

4128  i3 

48 

4944 

5857 

653o 

6960 

7i45   7081 

6764 

6i93 

5364 

4275  12 

49 

5i28 

6o37 

6706 

7i32 

73i3   7244 

6924 

6348 

55i5 

44ai  ii 

5o 

775312 

786217 

796882 

807304 

817480 

827407 

837083 

8465o3 

855665 

86456  7]  10 

5i 

5496 

6396 

7°57 

7475 

7648 

7571 

.7242 

6658 

58:6 

47i3|  9 

52 

5679 

6576 

7233 

«7647 

78i5 

7734 

74oi 

68i3 

5966 

486o]  8 

53 

5863 

6756 

7408 

7818 

7982 

7897 

756o 

6967 

61  17 

5oo6 

7 

54 

6o46 

6935 

7584 

799° 

8i5o 

8060 

77i9 

7122 

6267 

5i5i 

6 

55 

623o 

7114 

7759 

8161 

83i7 

8223 

7878 

7277 

6417 

5297 

5 

56 

64i3 

7294 

7935 

8333 

8484 

8386 

8o36 

743  1 

6567 

5443 

4 

5? 

6596 

7473 

8no 

85o4 

865i 

8549 

8i95 

7585 

67i8 

5589 

3 

58 

6780 

7652 

8285 

8675 

8818 

8712 

8354 

774o 

6868 

5734 

2 

59 

6963 

7832 

846o 

8846 

8985 

8875 

85i2 

7894 

7017 

588o 

I 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32° 

31° 

30J 

s 

Natural  Co-sines. 

i 

P  P.  „  t 
tol//3.o8 

3.02 

2.95 

2.88   s.8i 

t.75 

2.68   2.60 

2.53   2.46 

NATURAL    TANGENTS. 


12 


4 

x 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

58° 

59° 

o 

1.19175 

1.23490 

1.27994 

1.32704 

1.37638 

1.42815 

1.48256 

1.53986 

i.6oo33 

i  66428 

60 

I 

9246 

3563 

8071 

a785 

7722 

29o3 

8349 

4o85 

0137 

6538 

59 

2 

93:6 

3637 

8i48 

2865 

7807 

2$92 

8442 

4i83 

024l 

6647 

58 

3 

9387 

3710 

8225 

2946 

7891 

3o8o 

8536 

4281 

o345 

6757 

57 

4 

9457 

3784 

83o2 

3026 

7976 

3i69 

8629 

4379 

o44g 

6867 

56 

5 

9528 

3858 

8379 

3107 

8060 

3258 

8722 

447« 

o553 

6978 

55 

6 

9^99 

393i 

8456 

3i87 

8i45 

3347 

8816 

4576 

0657 

7088 

54 

7 

9669 

4oo5 

8533 

3268 

8229 

3436 

89o9 

4675 

0761 

7i98 

53 

8 

9740 

4079 

8610 

3349 

83i4 

3525 

9oo3 

4774 

o865 

73o9 

52 

9 

9811 

4i53 

8687 

343o 

8399 

36i4 

9°97 

4873 

o97o 

74i9 

5i 

10 

1.19882 

1.24227 

1.28764 

i.335ii 

1.38484 

1.43703 

i.49i9o 

1.54972 

1.61074 

1.67530 

5o 

ii 

9953 

43oi 

8842 

3592 

8568 

3792 

9284 

5071 

"79 

764i 

49 

12 

1.20024 

4375 

89i9 

3673 

8653 

388i 

9378 

5170 

1283 

7752 

48 

i3 

oogS 

4449 

8997 

3754 

8738 

397o 

9472 

5269 

1  388 

7863 

4? 

i4 

0166 

4523 

9o74 

3835 

8824 

4o6o 

9566 

5368 

i493 

7974 

46 

i5 

0237 

4597 

9l52 

3916 

8909 

4i49 

966i 

5467 

i598 

8o85 

45 

16 

o3o8 

4672 

9229 

3998 

8994 

4239 

9755 

5567 

1703 

8i96 

44 

i? 

°379 

4?46 

93°7 

4079 

9079 

4329 

9849 

5666 

1808 

83o8 

43 

18 

o45i 

4820 

9385 

4i6o 

9i65 

44i8 

9944 

5766 

i9i4 

8419 

42 

J9 

O522 

4895 

9463 

4242 

925o 

45o8 

i.5oo38 

5866 

20I9 

853i 

4i 

20 

1.20593 

1.24969 

i.2954i 

1.34323 

1.39336 

1.44598 

i.5oi33 

1.55966 

I.62I25 

1.68643 

4o 

21 

o665 

5o44 

96i8 

44o5 

9421 

4688 

0228 

6o65 

2230 

8754 

39 

22 

o736 

5n8 

9696 

4487 

95°7 

4778 

0322 

6i65 

2336 

8866 

38 

23 

0808 

5i93 

9775 

4568 

.  9593 

4868 

0417 

6265 

2442 

8979 

37 

24 

0879 

5268 

9853 

465o 

9679 

4958 

o5i2 

6366 

2548 

9°9; 

36 

25 

095  1 

5343 

993i 

4732 

9764 

5o4g 

0607 

6466 

2654 

92o3 

35 

26 

1023 

54i7 

i.3ooo9 

48i4 

985o 

5i39 

0702 

6566 

2760 

93i6 

34 

27 

1094 

5492 

0087 

4896 

9936 

5229 

0797 

6667 

2866 

9428 

33 

28 

1166 

5567 

0166 

4978 

1.40022 

5320 

o893 

6767 

2972 

954i 

32 

29 

1238 

5642 

0244 

5o6o 

oio9 

54io 

0988 

6868 

3o79 

9653 

3i 

3o 

I.2l3lO 

1.25717 

i.3o323 

i.35i4a 

i.4oi95 

i.455oi 

i.5io84 

1.56969 

i.63i85 

1.69766 

3o 

3i 

i382 

5792 

o4oi 

5224 

0281 

5592 

1179 

7069 

3292 

9879 

29 

32 

i454 

5867 

o48o 

53o7 

o367 

5682 

1275 

7170 

3398 

9992 

28 

33 

i526 

5943 

o558 

5389 

o454 

5773 

1370 

7271 

35o5 

1.70106 

27 

34 

i598 

6018 

0637 

5472 

o54o 

5864 

i486 

7372 

36i2 

0219 

26 

35 

1670 

6093 

0716 

5554 

0627 

5955 

i562 

7474 

37i9 

o332 

25 

36 

1742 

6169 

°795 

5637 

0714 

6o46 

i658 

7575 

3826 

o446 

24 

3? 

1814 

6244 

0873 

57i9 

0800 

6i37 

1754 

7676 

3934 

o56o 

23 

38 

1886 

63i9 

O952 

58o2 

0887 

6229 

i85o 

7778 

4o4i 

0673 

22 

39 

1959 

6395 

io3i 

5885 

o974 

6320 

1946 

7879 

4i48 

0787 

21 

4o 

I.22o3l 

1.26471 

i.3uio 

1.35968 

1.41061 

i.464ii 

i.52o43 

1.57981 

1.64256 

1.70901 

20 

4i 

2104 

6546 

II90 

6o5i 

n48 

65o3 

2139 

8o83 

4363 

ioi5 

J9 

42 

2176 

6622 

I269 

6i34 

1235 

6595 

2235 

8i84 

447i 

1129 

18 

43 

2249 

6698 

1  348 

6217 

l322 

6686 

2332 

8286 

4579 

1244 

i? 

44 

2321 

6774 

1427 

63oo 

i4o9 

6778 

2429 

8388 

4687 

i358 

16 

45 

2394 

6849 

i5o7 

6383 

i497 

8870 

2525 

8490 

4795 

i473 

i5 

46 

2467 

6925 

i586 

6466 

1  584 

6962 

2622 

8593 

4903 

1  588 

i4 

4? 

2539 

7001 

1666 

6549 

1672 

7o53 

2719 

8695 

5ou 

1702 

i3 

48 

26l2 

7077 

1745 

6633 

i759 

7i46 

2816 

8797 

5l2O 

1817 

12 

49 

2685 

7i53 

i825 

6716 

1847 

7238 

2913 

8900 

5228 

1932 

II 

5o 

1.22768 

1.27230 

i.3i9o4 

i.368oo 

1.41934 

i.4733o 

i.  53oio 

1.59002 

1.65337 

1.72047 

IO 

5i 

283i 

73o6 

1984 

6883 

2O22 

7422 

3107 

9106 

5445 

ai63 

9 

52 

2904 

7382 

2064 

6967 

2IIO 

75i4 

32o5 

9208 

5554 

2278 

8 

53 

2977 

7458 

2144 

7o5o 

2I98 

7607 

33o2 

93u 

5663 

2393 

7 

54 

3o5o 

7535 

2224 

7i34 

2286 

7699 

34oo 

94i4 

5772 

2609 

6 

55 

3i23 

7611 

23o4 

7218 

2374 

7792 

3497 

95i7 

588i 

2625 

5 

56 

8196 

7688 

2384 

7302 

2462 

7885 

3595 

9620 

599o 

2741 

4 

5? 

3270 

7764 

2464 

7386 

255o 

7977 

3693 

9723 

6o99 

2867 

3 

58 

3343 

7841 

2544 

7470 

2638 

8070 

379i 

0826 

62O9 

2973 

2 

5  9 

34i6 

7917 

262^ 

7554 

2726 

8i63 

3888 

993o 

63i8 

3o89 

I 

39° 

38° 

37° 

36° 

35° 

34° 

33° 

32°    31° 

30° 

a 

Natural  Co-tangents. 

P.  P. 

to  I".1'80 

1.25 

i.3i 

r.37 

i.44 

i.5i 

i.59 

1.68 

1.78 

1.88 

NATURAL    SINES. 


1   60° 

61° 

62° 

63° 

64° 

65° 

66° 

67°  1  68° 

69° 

o 

866025 

8-74620 

882948 

89ioo7 

898794 

9o63o8 

9i3545 

92o5o5'  92718^ 

93358o 

60 

i 

6171 

4?6i 

3o84 

n39 

8922 

643  1 

3664 

0618 

7293 

3685  59 

2 

63i6 

4902 

3221 

1270 

9o49 

6554 

3782 

0732 

7402 

378958 

3 

646i 

5o42 

3357 

1402 

9i76 

6676 

39oo 

o846 

75io 

389'-)  5  7 

L 

6607 

5i83 

3493 

i534 

93o4 

6799 

4oi8 

o959 

76i9 

3997  56 

t 

6762 

5324 

3629 

1666 

943i 

6922 

4i36 

1072 

7728 

4ioi  55 

6 

6897 

5465 

3766 

1798 

9558 

7044 

4254 

n85 

7836 

4204  54 

7 

7042 

56o5 

3902 

1929 

9685 

7166 

4372 

i299 

7945 

43o8  53 

8 

7187 

5746 

4o38 

2061 

9812 

7289 

449o 

1412 

8o53 

44i2 

52 

9 

733i 

5886 

4i74 

2192 

9939 

?4n 

46o7 

i525 

8161 

45i5 

5i 

10 

867476 

8-76026 

884309 

892323 

9ooo65 

907533 

9i4725 

92i638 

92827O 

9346i9 

5o 

ii 

7621 

6i67 

4445 

2455 

OI92 

7655 

4842 

1750 

8378 

4722 

49 

12 

7765 

63o7 

458i 

2586 

o3i9 

7777 

496o 

i863 

8486 

4826 

48 

l2 

7910 

6447 

4717 

2717 

o44-5 

7899 

5o77 

i976 

8594 

4929 

47 

i4 

8o54 

6587 

4852 

2848 

0572 

8021 

5i94 

2088 

8702 

5o32 

46 

i5 

8199 

6727 

4988 

2979 

o698 

8i43 

53n 

2201 

8810 

5i35 

45 

16 

8343 

6867 

5i23 

3no 

0825 

8265 

5429 

23l3 

89i7 

5238 

44 

17 

8487 

7006 

5258 

324l 

o95i 

8387 

5546 

2426 

9025 

534i 

43 

18 

863a 

7i46 

5394 

337i 

io77 

85o8 

5663 

2538 

9i33 

5444 

42 

*9 

8776 

•7286 

5529 

35o2 

1203 

863o 

5779 

265o 

9240 

5547 

4i 

20 

868920 

877425 

885664 

893633 

9oi329 

9o875i 

9i5896 

922762 

929348 

93565o 

4o 

21 

9064 

7565 

5-799 

3763 

1455 

8872 

6oi3 

2875 

9455 

6762 

39 

22 

9207 

77o4 

5934 

3894 

i58i 

8994 

6i3o 

2986 

9-662 

5855 

38 

23 

935i 

7844 

6069 

4024 

I7°7 

9n5 

6246 

3o98 

9669 

5957 

37 

24 

9495 

7983 

6204 

4i54 

i833 

9236 

6363 

3210 

9776 

6060 

36 

26 

9639 

8122 

6338 

4284 

i958 

9357 

6479 

3322 

9884 

6162 

35 

26 

9782 

8261 

6473 

44i5 

2084 

9478 

6595 

3434 

999° 

6264 

34 

27 

9926 

84oo 

6608 

4545 

2209 

9599 

67I2 

3545 

93oo97 

6366 

33 

28 

870069 

8539 

6742 

4675 

2335 

9720 

6828 

3657   02°4 

6468 

32 

29 

O2I2 

8678 

6876 

48o5 

2460 

984i 

6944 

3768|  o3n 

657o 

3i 

3o 

87o356 

8788i7 

88-7011 

894934 

9o2585 

9o996i 

9i7o6o 

923880  930418 

936672 

3o 

3i 

o499 

8956 

7i45 

5o64 

2710 

9ioo82 

7i76 

399i 

0624 

6774 

29 

32 

0642 

9095 

7279 

5i94 

2836 

O2O2 

7292 

4lO2 

o63i 

6876 

28 

33 

o785 

9233 

74i3 

5323 

296l 

o323 

74o8 

42i3 

o737 

6977 

2-7 

34 

0928 

9372 

7548 

5453 

3o86 

0443 

7523 

4324 

o843 

7°79 

26 

35 

1071 

95io 

768i 

5582 

3210 

o563 

7639 

4435 

o95o 

7i8i 

23 

36 

I2l4 

9649 

78i5 

5712 

3335 

o684 

7755 

4546 

io56 

-7282 

24 

3? 

i357 

9787 

7949 

584i 

346o 

0804 

787o 

4657 

1162 

7383 

23 

38 

1499 

9925 

8o83 

5970 

3585 

o924 

7986 

4768 

1268 

7485 

22 

39 

1642 

88oo63 

82I7 

6099 

37°9 

io44 

8101 

4878 

i374 

7586 

21 

4o 

871784 

880201 

88835o 

896229 

9o3834 

9i  i  i  64 

9i82i6 

924989 

93i48o 

937687 

2O 

4i 

1927 

o339 

8484 

6358 

3958 

1284 

833i 

5099 

1  586 

7788 

19 

42 

2069 

o477 

86i7 

6486 

4o83 

i4o3 

8446 

52IO 

i69i 

7889 

18 

43 

2212 

o6i5 

8751 

66i5 

4207 

i523 

856i 

532o|   1797 

799o 

17 

44 

2354 

o753 

8884 

6744 

433i 

i643 

8676 

543o   1902 

8o9i 

16 

45 

2496 

0891 

9017 

6873 

4455 

1762 

879i 

554i   2008 

8i9i 

i5 

46 

2638 

1028 

9i5o 

7001 

4579 

1881 

89o6 

565i   2ii3 

8292 

i4 

.4? 

2780 

1166 

9283 

7i3o 

47o3 

2OOI 

902I 

5761   2219 

8393 

i3 

48 

2922 

i3o3 

94i6 

7258 

4827 

2120 

9i35 

5871   2324 

8493 

12 

49 

3o64 

i44i 

9549 

7387 

495i 

2239 

925o 

5980   2429 

8593 

II 

5o 

873206 

88i578 

889682 

8975i5 

505075 

9i2358 

9i9364 

926090  932534 

938694 

ro 

5i 

334y 

1716 

9815 

7643 

5i98 

2477 

9479 

6200   2639 

8-794 

9 

52 

3489 

i853 

9948 

7771 

5322 

2596 

9593 

63io   2744 

8894 

8 

53 

363i 

1990 

89oo8o 

79oo 

5445 

2715 

97o7 

64i9   2849 

8994 

7 

54 

3772 

2127 

02l3 

8028 

5569 

2834 

982I 

6529   2954 

9094 

6 

55 

39i4 

2264 

o345 

8i56 

5692 

2953 

9936 

6638;   3o58 

9i94 

5 

56 

4o55 

24OI 

o478 

8283 

58i5 

3072 

92oo5o 

6747i   3i63 

9294 

4 

5? 

4196 

2538 

0610 

84n 

5939 

3i9o 

oi64 

6857   3267 

9394 

3 

58 

4338 

2674 

0742 

8539 

6062 

33o9 

0277 

6966   3372 

9493 

2 

59 

4479 

2811 

o874 

8666 

6i85 

3427 

o39i 

7o75   3476 

9593 

I 

29° 

28°   27°   26° 

25°   24°   23°   22°   21° 

20° 

0 

Natural  Co-sines. 

'•£ 

££>39 

2.3l 

2.24   2.16 

2.O9 

2.OI 

i.93 

1.86 

1.78 

1.70 

NATURAL    TANGENTS. 


J 

n 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

69° 

0 

1.73205 

i.8o4o5 

1.88073 

1.96261 

2.o5o3o 

2.i445i 

2.  246o4 

2.35585 

2.47509 

2.60509 

60 

i 

332i 

0529 

82o5 

6402 

5i82 

46i4 

4780 

5776 

7716 

o736 

59 

2 

3438 

o653 

8337 

6544 

5333 

4777 

4956 

5967 

7924 

0963 

58 

3 

3555 

0777 

8469 

6685 

5485 

494o 

5i32 

6i58 

8x32 

1190 

57 

4 

367i 

0901 

8602 

6827 

5637 

5io4 

53o9 

6349 

834o 

i4i8 

56 

5 

3788 

1025 

8734 

6969 

579o 

5268 

5486 

654i 

8549 

1  646 

55 

6 

3905 

n5o 

8867 

7111 

5942 

5432 

5663 

6733 

8758 

1874 

54 

7 

4O22 

1274 

9000 

7253 

6094 

5596 

584o 

6925 

8967 

2103 

53 

8 

4i4o 

i399 

9i33 

7395 

6247 

5760 

6018 

7118 

9i77 

2332 

52 

9 

4257 

i524 

9266 

7538 

64oo 

5925 

6196 

73u 

9386 

256i 

5i 

10 

i.74375 

1.81649 

1.89400 

1.97681 

2.o6553 

2.16090 

2.26374 

2.37504 

2.4959-7 

2.62791 

5o 

ii 

4492 

1774 

9533 

7823 

67o6 

6255 

6552 

7697 

98o7 

3021 

49 

12 

46io 

1899 

9667 

7966 

6860 

6420 

673o 

7891 

2.5ooi8 

3252 

48 

i3 

4728 

2O25 

9801 

8110 

7oi4 

6585 

6909 

8o84 

0229 

3483 

47 

i4 

4846 

2i5o 

9935 

8253 

7i67 

675i 

7o88 

8279 

o44o 

37i4 

46 

i5 

4964 

2276 

1.90069 

8396 

732I 

6917 

7267 

8473 

o652 

3945 

45 

16 

5o82 

24O2 

0203 

854o 

7476 

7083 

7447 

8668 

0864 

4177 

44 

«7 

5200 

2528 

o337 

8684 

763o 

7249 

7626 

8863 

io76 

44io 

43 

18 

53i9 

2654 

0472 

8828 

7785 

74i6 

7806 

9o58 

1289 

4642 

4a 

*9 

5437 

2780 

0607 

8972 

7939 

7582 

7987 

9253 

I5O2 

4875 

4i 

20 

i.75556 

1.82906 

1.90741 

1.99116 

2.08094 

2.17749 

2.28167 

2.39449 

2.5i7i5 

2.65iO9 

4o 

21 

5675 

3o33 

0876 

9261 

825o 

7916 

8348 

9645 

1929 

5342 

39 

22 

5794 

3i59 

'  IOI2 

9406 

84o5 

8o84 

8528 

984i 

2l42 

5576 

38 

23 

59i3 

3286 

1147 

955o 

856o 

825i 

8710 

2.4oo38 

2357 

58ii 

37 

24 

6o32 

34i3 

1282 

9695 

87i6 

8419 

8891 

0235 

257I 

6o46 

36 

25 

6i5i 

354o 

i4i8 

984i 

8872 

8587 

9o73 

o432 

2786 

6281 

35 

26 

6271 

3667 

1  5  54 

9986 

9028 

8755 

9254 

0629 

3ooi 

65i6 

34 

27 

6390 

3794 

1690 

2.00l3l 

9184 

8923 

9437 

0827 

32i7 

6752 

33 

28 

65io 

3922 

1826 

0277 

934i 

9092 

9619 

IO25 

3432 

6989 

32 

29 

663o 

4049 

1962 

0423 

9498 

9261 

9801 

1223 

3648 

7225 

3i 

3o 

1.76749 

1.84177 

1.92098 

2.00669 

2.09654 

2.19430 

2.29984 

2.4i4ai 

2.53865 

2.67462 

3o 

3i 

6869 

43o5 

2235 

0715 

9811 

9599 

2.30167 

1620 

4082 

7700 

29 

32 

6990 

4433 

2371 

0862 

9969 

9769 

o35i 

1819 

4299 

7937 

28 

33 

7110 

456i 

25o8 

1008 

2.10126 

9938 

o534 

2019 

45i6 

8i75 

27 

34 

723o 

4689 

2645 

n55 

0284 

2.20108 

0718 

2218 

4734 

84i4 

26 

35 

735i 

48i8 

2782 

1302 

o442 

0278 

0902 

2418 

4952 

8653 

25 

36 

7471 

4946 

2920 

i449 

0600 

o449 

1086 

2618 

5170 

8892 

24 

3? 

7592 

5o75 

3o57 

i596 

o758 

0619 

1271 

2819 

5389 

9i3i 

23 

38 

77i3 

52o4 

3i95 

1743 

0916 

0790 

i456 

3019 

56o8 

937i 

22 

39 

?834 

5333 

3332 

1891 

io75 

0961 

i64i 

3220 

5827 

9612 

21 

4o 

1.77955 

1.85462 

1.93470 

2.02039 

2.II233 

2.2II32 

2.31826 

2.43422 

2.56o46 

2.69853 

2O 

4i 

8077 

559i 

36o8 

2187 

1392 

i3o4 

2OI2 

3623 

6266 

2.70094 

*9 

42 

8198 

5720 

3746 

2335 

i552 

1475 

2I97 

3825 

6487 

o335 

18 

43 

8319 

585o 

3885 

2483 

i7n 

1647 

2383 

4027 

6707 

o577 

*7 

44 

844i 

5979 

4oa3 

263i 

i87i 

1819 

2570 

423o 

6928 

0819 

16 

45 

8563 

6109 

4162 

2780 

2o3o 

1992 

2756 

4433 

7i5o 

1062 

i5 

46 

8685 

6239 

43oi 

2929 

2190 

2164 

2943 

4636 

737i 

i3o5 

i4 

4? 

8807 

6369 

444o 

3078 

235o 

2337 

3i3o 

4839 

7593 

1  548 

i3 

48 

8929 

6499 

4579 

3227 

25ll 

25lO 

33i7 

5o43 

78i5 

I792 

f 

12 

49 

9o5i 

663o 

4718 

3376 

2671 

2683 

35o5 

5246 

8o38 

2o36 

II 

5o 

i-79I?4 

1.86760 

1.94858 

2.o3526 

2.12832 

2.22857 

2.33693 

2.4545i 

2.58261 

2.  7228l 

IO 

5i 

9296 

6891 

4997 

3675 

2993 

3o3o 

388i 

5655 

8484 

2526 

9 

52 

9419 

7021 

5i37 

3825 

3i54 

3204 

4o69 

586o 

8708 

277I 

8 

53 

9542 

7i52 

5277 

3975 

33i6 

3378 

4258 

6o65 

8932 

3oi7 

7 

54 

9665 

7283 

54i7 

4i25 

3477 

3553 

4447 

6270 

9i56 

3263 

6 

55 

9788 

74i5 

5557 

4276 

3639 

3727 

4636 

6476 

9381 

35o9 

5 

56 

9911 

7546 

5698 

4426 

38oi 

3902 

4825 

6682 

9606 

3756 

4 

5? 

i.8oo34 

7677 

5838 

4577 

3963 

4077 

5oi5 

6888 

983i 

4oo4 

3 

58 

oi58 

7809 

5979 

4728 

4i25 

4252 

52o5 

7095 

2.60057 

425i 

2 

59 

0281 

794i 

6120 

4879 

4288 

4428 

,  5395 

7302 

0283 

4499 

I 

29° 

28° 

27° 

26° 

25° 

24° 

23° 

22° 

21° 

20° 

£ 

Natural  Co-tangents. 

33 

P  P. 

tol".a'°° 

2.13 

2.27 

2.44 

2.62 

2.82 

3.o5 

3.3i 

3.6i 

3.95 

130 


NATURAL    SINES. 


£ 

70° 

71° 

72° 

73° 

74° 

75° 

763 

77° 

78° 

79° 

o 

I 

939693 
9792 

9455i9 
56i3 

95io57 
n46 

966306  961262 
6390   i  342 

966926 
6001 

970296 
o366 

97437o 
4435 

978i48 
8208 

98i627|6o 
1683  5q 

2 

9891 

57o8 

1236 

6475[   1422 

6076 

o436 

45oi 

8268 

i738 

58 

(. 

999  * 

58o2 

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656o 

1502 

6i5i 

o5o6 

4566 

8329 

I793 

57 

L 

940090 

5897 

i4i5 

6644 

i582 

6226 

o577 

463i 

8389 

1849 

56 

I 

0189 

599i 

i5o5 

6-729 

1662 

63oi 

o647 

4696 

8449 

1904 

55 

6 

0288 

6o85 

1  5g4 

68i4 

i74i 

6376 

o7i6 

476i 

85o9 

1969 

54 

7 

o387 

6180 

1  684 

6898 

1821 

645  1 

o786 

4826 

8569 

20l4 

53 

8 

o486 

6274 

i773 

6983 

I9OI 

6626 

o856 

489i 

8629 

2O69 

52 

9 

o585 

6368 

1862!   7067 

i98o 

6600 

0926 

4956 

8689 

2123 

5i 

10 

940684 

946462 

961961 

957i5i 

962059 

956675 

97°995 

975o2o 

978748 

982i78 

5o 

ii 

0782 

6555 

2o4o 

7235 

2139 

6749 

io65 

5o85 

8808 

2233 

49 

12 

0881 

6649 

2129 

73i9 

2218 

6823 

ii34 

5i49 

8867 

228-7 

48 

i3 

0979 

6743 

2218 

74o4 

2297 

6898 

1204 

52i4 

891- 

3342 

47 

i4 

1078 

6837 

2307 

7487 

2376 

6972 

I273 

5278 

8986 

2396 

46 

i5 

1176 

6930 

2396 

757i 

2455 

7o46 

1  342 

5342 

9o45 

245o 

45 

16 

1274 

7024 

2484 

7655 

2534 

•7120 

i4n 

54o6 

9io5 

25o5 

M 

i? 

I3?2 

7117 

2573 

7739 

*  26i3 

7ig4 

i48o 

547i 

9i64 

2559 

43 

18 

1471 

7210 

2661 

7822 

2692 

7268 

i549 

5535 

9223 

26i3 

42 

'9 

i569 

73o4 

275© 

•7906 

2770 

7342 

1618 

5598 

9282 

2667 

4i 

20 

941666 

947397 

952838 

95799° 

962849 

9674i5 

97i687 

976662 

97934i 

0.82-721 

4o 

21 

1764 

7490 

2926 

8o73 

2928 

7489 

i755 

5-726 

9399 

2774 

39 

22 

1862 

7583 

3oi5 

8i56 

3oo6 

7562 

1824 

579o 

9458 

2828 

38 

23 

1960 

7676 

3io3|   8239 

3o84 

7636 

i893 

5853 

95l7 

2882 

37 

24 

2057 

7768 

3i9n   8323 

3i63 

77°9 

i96i 

59i7 

9575 

2935 

36 

25 

2i55 

7861 

3279 

84o6 

324i 

7782 

2O29 

598o 

9634 

2989 

35 

26 

2252 

7954 

3366 

8489 

33i9 

7856 

2098 

6o44 

9692 

3o42 

34 

27 

235o 

,  8o46 

3454 

8572 

3397 

7929 

2l66 

610-7 

975o 

3o96 

33 

28 

2447 

8i39 

3542 

8654 

3475 

8002 

2234 

6i7o 

98o9 

3i49 

32 

29 

2544 

823i 

3629 

8737 

3553 

8o75 

2302 

6233 

9867 

3*02 

3i 

3o 

942641 

948324 

9537«7 

95882o 

96363o 

968i48 

972370 

976296 

979925 

983255 

3o 

3i 

2739 

84i6 

38o4 

89O2 

37o8 

8220 

2438 

6359 

9983 

33o8 

29 

32 

a836 

85o8 

3892   8985 

3786 

8293 

25o6 

6422 

98oo4i 

336i 

28 

33 

2932 

8600 

3979 

9o67 

3863 

8366 

2573 

6485 

0098 

34x4 

27 

34 

3029 

8692 

4o66 

9i5o 

394i 

8438 

2641 

6547 

oi56 

3466 

26 

35 

3i26 

8784 

4:53 

9232 

4oi8 

85n 

2708 

6610 

0214 

35i9 

25 

36 

3223 

8876 

4240 

93i4 

4o95 

8583 

2776 

66-72 

O27I 

'  357i 

24 

3? 

33i9 

8968 

4327 

9396 

4i73 

8656 

2843 

6735 

o32g 

3624 

23 

38 

34i6 

9o59 

44i4 

9478 

425o 

8728 

291  1 

6797 

o386 

3676 

22 

39 

35i2 

9i5i 

45oi 

956o 

4327 

8800 

2978 

6859 

o443 

3729 

21 

4o 

943609 

949243 

954588 

959642 

9644o4  968872 

973o45 

97692i 

980600 

98378i 

20 

4i 

37o5 

9334 

4674 

9724 

448  i   8944 

3lI2 

6984 

o558 

3833 

'9 

42 

38oi 

9425 

476i 

98o5 

4557   9oi6 

3i79 

7o46 

o6i5 

3885 

18 

43 

3897 

95l7 

4847 

9887 

4634   9o88 

3246 

-7108 

06-72 

3937 

'7 

44 

3993 

96o8 

4934 

9968 

47n   9i59 

33i3 

7i69 

0728 

3989 

16 

45 

4089 

9699 

5020 

96oo5o 

4787   923i 

3379 

723l 

o785 

4o4i 

i5 

46 

4i85 

9-790 

5io6 

oi3i 

4864   93o2 

3446 

7293 

0842 

4092 

i4 

47 

4281 

9881 

5192 

0212 

494o   9374 

35i2 

7354 

0899 

4i44 

i3 

"48 

4376 

9972 

5278 

0294 

5oi6   9446 

3579 

74i6 

o955 

4196 

12 

49 

4472 

95oo63 

5364 

o375 

5o93   95i7 

3645 

7477 

1012 

4247 

II 

5o 

944568 

95oi54 

95545o 

96o456 

966169  969588 

9737i2 

977539 

981068 

984298 

IO 

5i 

4663 

0244 

5536 

o537 

5245   9659 

3778 

76oo 

1124 

435o 

9 

5a 

4758 

o335 

5622 

0618 

532i   973o 

3844 

•7661 

1181 

44oi 

8 

53 

4854 

042  5 

57°7 

o698 

5397   98oi 

3910 

7722 

I237 

4452 

7 

54 

4949 

o5i6 

5793 

°779 

5473!   9872 

3976 

7783 

I293 

45o3 

6 

55 

5o44 

0606 

5879 

0860 

5548;   9943 

4042 

7844 

1  349 

4554 

5 

56 

5i39 

0696 

5964 

o94o 

5624  97ooi4 

4io8 

79o5 

i4o5 

46o5 

4 

57 

5234 

o786 

6o4g 

1021 

57oo   oo84 

4i73 

7966 

i46o 

4656 

3 

58 

5329 

o877 

6i34 

IIOI 

5775:  oi55 

4239 

8026   i5i6 

47°7 

2 

59 

5424 

096-7 

6220 

1181 

585o   0225 

43o5 

8o87|   i572 

4757 

I 

19° 

18° 

17° 

16° 

15°   14° 

13° 

12° 

11° 

10° 

d 

Natural  Co-sines. 

i 

££'•«» 

i.54 

i.46 

i.38 

:.3o 

I  .21 

i.i3 

1.  06 

o-97 

0.88 

NATURAL 


GENTS. 


131 


j 

70° 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

o 

2.74748 

2.90421 

3.07768 

3.27o85 

3.4874i 

3.732o5 

4.010-78 

4.33i48 

4-7o463 

5.14455 

60 

I 

4997 

0696 

8073 

7426 

9I25 

364o 

i576 

3723 

u37 

6266 

59 

2 

6246 

0971 

8379 

7767 

95o9 

4o75 

2074 

43oo 

i8i3 

6068 

58 

q 

6496 

1246 

8685 

8io9 

9894 

4612 

2574 

4879 

2490 

6863 

57 

4 

5746 

1623 

899i 

8462 

3.5o279 

4g5o 

3o76 

5459 

3i7o 

7671 

56 

c 

6996 

1799 

9298 

8795 

o666|   5388 

3578 

6o4o 

385i 

848o 

55 

6 

624-7 

2O76 

96o6 

9l39 

io53 

6828 

4o8i 

6623 

4534 

9293 

54 

7 

6498 

2354 

99i4 

9483 

i44i 

6268 

4586 

7207 

52I9 

5.20I07 

53 

8 

675o 

2632 

3.10223 

9829 

i829 

6-709 

6092 

7793 

59o6 

O925 

52 

9 

7002 

2910 

o532 

3.3oi74 

22I9 

7162 

5599 

838i 

6595 

i744 

5i 

10 

2.77264 

2.93189 

3.io842 

3.3o52i 

3  526o9 

3.77595 

4.0610-7 

4.38969 

4.77286 

5.22566 

5o 

ii 

7607 

3468 

ii53 

0868 

3ooi 

8o4o 

6616 

956o 

7978 

339i 

49 

12 

7761 

3748 

i464 

1216 

3393 

8485 

7I27 

4.40162 

8673 

4218 

48 

i3 

8oi4 

4028 

1776 

i565 

3785 

8931 

7639 

0746 

937o 

5o48 

47 

i4 

8269 

43o9 

2087 

i9i4 

4i79 

9378 

8162 

i34o 

4.80068 

588o 

46 

16 

8523 

459I 

24oo 

2264 

4573 

9827 

8666 

I936 

o769 

67i5 

45 

16 

8778 

4872 

2713 

2614 

4968 

3.802-76 

9182 

2534 

i47i 

7553 

44 

17 

9o33 

5i55 

3027 

2965 

5364 

0-726 

9699 

3i34 

2I75 

8393 

43 

18 

9289 

5437 

334i 

33i7 

576i 

n77 

4.10216 

3735 

2882 

9235 

42 

'9 

9545 

6-721 

3656 

367o 

6i59 

i63o 

o736 

4338 

359o 

5.3oo8o 

4i 

20 

2.798O2 

2.96004 

3.i3972 

3.34023 

3.56557 

3.82083 

4.ii256'4.44942 

4.843oo 

5.3o928 

4o 

21 

2.8oo59 

6288 

4288 

4377 

6957 

2537 

1778 

5548 

5oi3 

1-7-78 

39 

22 

o3i6 

6573 

46o5 

4732 

7357 

2992 

2301 

6i55 

5727 

263i 

38 

23 

0674 

6858 

4922 

5o87 

7758 

3449 

2826 

6764 

6444 

3487 

37 

24 

o833|   7144 

6240 

5443 

8160 

3906 

335o 

7374 

-7162 

4345 

36 

25 

:o9i 

743o 

5558 

58oo 

8662 

4364 

3877 

7986 

•7882 

6206 

35 

26 

i35o 

77i7 

5877 

6168 

8966 

4824 

44o5 

8600 

86o5 

6o7o 

34 

27 

1610 

8oo4 

6i97 

65i6 

937o 

6284 

4934 

92l5 

933o 

6936 

33 

28 

1870 

8292 

65i7 

6875 

9775 

5745 

5465 

9832 

4.9oo56 

78o5 

32 

29 

2130 

858o 

6838 

7234 

3.6oi8i 

6208 

699-7 

4.5o45i 

o785 

8677 

3i 

3o 

2.8239I 

2.98868 

3.i7i59 

3.37594  3.6o588 

3.8667i 

4.i653o 

4.61071 

4.91616 

5.39552 

3o 

3i 

2653 

9168 

748t 

7955;  o996 

7  1  36 

7o64 

i693 

2249 

5.4o429 

29 

32 

29i4 

9447 

78o4 

8317 

i4o5 

7601 

•7600 

23i6 

2984 

i3o9 

28 

33 

3i76 

9738 

812-7 

8679 

1814 

8068 

8i37 

294i 

372I 

2I92 

27 

34 

3439 

3.00028 

845  1 

2224 

8536 

8675 

3568 

446o 

3o77 

26 

35 

3702 

0319 

8775 

94o6 

2636 

9004 

9216 

4i96 

6201 

3966 

25 

36 

3965 

06  1  1 

9ioo 

9771 

3o48 

9474 

9756 

4826 

5945 

4857 

24 

37 

4229 

o9o3 

9426 

3.4oi36 

346i 

9945 

4.20298 

5458 

669o 

6761 

23 

38 

4494 

n96 

9752 

0602 

3874 

3.90417 

0842 

6o9i 

7438 

6648 

22 

39 

4768 

i489 

3.20O79 

o869 

4289 

0890 

i387 

6726 

8188 

7548 

21 

4o 

2.85oa3 

3.oi783 

3.2o4o6 

3.4i236 

3.647o5 

3.9i364 

4.21933 

4.57363 

4-9894o 

5.4845i 

20 

4i 

6289 

2077 

o734 

1604 

5l2I 

1839 

2481 

8001 

9695 

9356 

ig 

42 

5555 

2372 

io63 

I973 

5538 

23i6 

3o3o 

864i 

5.oo45i 

6.60264 

18 

43 

6822 

266-7 

i392 

2343 

5957 

2793 

358o 

9283    1210 

1176 

I7 

44 

6o89 

2963 

I722 

27l3 

6376 

327I 

4l32 

9927 

i97i 

2000 

16 

45 

6356 

3260 

2053 

3o84 

6796 

375i 

4685 

4.60672 

2734 

3007 

i5 

46 

6624 

3556 

2384 

3456 

72I7 

4232 

6239 

I2I9 

3499 

3927 

i4 

47 

6892 

3854 

27l5 

3829 

7638 

47i3 

5795 

1868 

4267 

485i 

i3 

48 

7161 

4162 

3o48 

4202 

8061 

6196 

6352 

25l8 

5o37 

5777 

12 

49 

743o 

445o 

338i 

4576 

8485 

568o 

6911 

3l7I 

58o9 

6706 

II 

5o 

2.87700 

3*oA'74Q 

3.237i4 

3.4495i 

3.68909 

3.96i65 

4.2747i 

4.63825 

5.o6584 

5.57638 

10 

5i 

7970 

5o49 

4o49 

5327 

9335 

6661 

8o32 

448o 

736o 

8573 

9 

62 

8240 

5349 

4383 

57o3 

976i 

7i39 

8696 

5i38 

8i39 

95n 

8 

53 

85  1  1 

5649 

47r9 

6080 

3.7oi88 

7627 

9169 

5797 

892I 

6.60462 

7 

54 

8783 

595o 

5o55 

6458 

0616 

811-7 

9724 

6458 

97o4 

i397 

6 

55 

9o55 

6262 

5392 

6837 

io46 

86o7 

4.30291 

7121  5.io49o   a344 

5 

56 

9327 

6554 

5729 

7216 

i476 

9°99 

0860 

7786   1270   3a95 

4 

57 

96oo 

6857 

6o67 

7596 

190-7 

9592 

i43o   8462   2069   4248 

3 

58 

9873 

7160 

64o6 

7977 

23384.00086 

2001    9I2I1    2862    5205   2 

69 

2.9oi47 

7464 

6745 

8359 

277l|    0682 

2573   979i   3658   6166  i 

19° 

18° 

17° 

16° 

15°  !  14° 

13°    12°    11°    10° 

.  ' 

Natural  Co-tangents. 

to*  I"'.4'35 

4.8a 

5.36 

6.01 

6.  -79 

7.73 

8.90 

10.35 

12.  2O 

i4.6o 

! 

132 


NATURAL    SINES. 


1 

H 

80° 

81° 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

O 

848o8 

987688 

990268 

992546 

994522 

99619-5 

997564 

99863o 

99939i 

999848 

[JO 

I 

4858 

7734 

o3o9 

2582 

4552 

6220 

7584 

8645 

94oi 

9853 

59 

2 

4909 

7779 

o34g 

2617 

4583 

6245 

76o4 

8660 

94n 

9358 

58 

3 

4959 

7824 

0389 

2652 

46i3 

6270 

7625 

8675 

942I 

9863 

57 

4 

5009 

7870 

0429 

2687 

4643 

6295 

7645 

869o 

943i 

9867 

56 

5 

SoSg 

79i5 

0469 

2722 

4673 

6320 

7664 

87o5 

944i 

9872 

55 

6 

5109 

7960 

oSog 

275? 

47o3 

6345 

7684:  8719 

945o 

9877 

54 

7 

5i59 

8oo5 

o549 

2792 

4733 

637o 

77o4 

8734 

946o 

9881 

53 

8 

5209 

8o5o 

oSSg 

2827 

4762 

6395 

7724 

8749 

9469 

9886 

52 

9 

5a59 

8o94 

0629 

2862 

4792 

64i9 

7743 

8763 

9479 

9890 

5i 

10 

985309 

988i39 

990669 

992896 

994822 

996444 

997763 

998778 

999488 

9V9894 

5o 

ii 

5358 

8i84 

0708 

293i 

485i 

6468 

7782 

8792 

9497 

9898 

49 

12 

54o8 

8228 

o748 

2966 

488  1 

6493 

7801 

8806 

95°7 

99o3 

43 

i3 

5457 

8273 

0787 

3ooo 

4910 

65i7 

7821 

8820 

95i6 

99°7 

47 

i4 

55o7 

83i7 

0827 

3o34 

4939 

654i 

7840 

8834 

95a5 

99io 

46 

i5 

5556 

8362 

0866 

3o68 

4969 

6566 

7869 

8848 

9534 

99i4 

45 

16 

56o5 

84o6 

0905 

3io3 

4998 

6590 

7878 

8862 

9542 

99i8 

44 

*7 

5654 

845o 

0944 

3i37 

5o27 

66i4 

7897 

8876 

955i 

9-932 

43 

18 

57o3 

8494 

0983 

3i7i 

5o56 

6637 

7916 

8890 

956o 

9925 

42 

J9 

575a 

8538 

IO22 

32o5 

5o84 

6661 

7934 

89o4 

9568 

9929 

4i 

20 

985801 

98858a 

991061 

993238 

995n3 

996685 

997953 

998917 

999577 

999932 

4o 

21 

585o 

8626 

IIOO 

3272 

5i42 

6709 

7972 

893i 

9585 

9936 

39 

23 

5899 

8669|   n38,   33o6 

5i7o 

6732 

799° 

8944 

9594 

9939 

38 

23 

5947 

8713   1177!   3339 

5i99 

6756 

8008 

8957 

96o2 

9942 

37 

24 

5996 

8756   1216'   3373 

5227 

6779 

8027 

8971 

96io 

9945 

36 

25 

6o45 

8800 

1254 

34o6 

5256 

6802 

8o45 

8984 

96i8 

9948 

35 

26 

6093 

8843 

I292 

3439 

5284 

6825 

8o63 

8997 

9626 

995i 

34 

27 

6i4i 

8886 

i33i 

3473 

53i2 

6848 

8081 

9010 

9634 

9954 

33 

28 

6189 

893o 

i369 

35o6 

534o 

6872 

8099 

9023 

9642 

9957 

32 

29 

6238 

8973 

1407 

3539 

5368 

6894 

8117 

9o35 

965o 

9959 

3i 

3o 

986286 

989oi6 

99i445 

993572 

995396 

996917 

998135 

999048 

999657 

999962 

3o 

3i 

6334 

9o59 

i483 

36o5 

5424 

6940 

8i53 

9061 

9665 

9964 

29 

32 

638i 

9102 

l52I 

3638 

5452 

6963 

8170 

9°73 

96-72 

9967 

28 

33 

6429 

9i45 

i558 

367o 

5479 

6985 

8188 

9o86 

9680 

9969 

27 

34 

6477 

9187   1596 

37o3 

55o7 

7008 

82o5 

9o98 

9687 

9971 

26 

35 

6525 

9230   i634 

3735 

5535 

7o3o 

8223 

9i  ii 

9694 

9974 

25 

36 

6572 

9272   1671 

3768 

5562 

7o53 

8240 

9I2: 

97oi 

9976 

24 

37 

6620 

93i5'   I7o9 

38oo 

5589 

7075 

8257 

9i35 

97°9 

9978123 

38 

6667 

9357 

1746 

3833 

56i7 

7097 

8274 

9147 

97i6 

9980 

22 

39 

6714 

9399 

I783 

3865 

5644 

7119 

8291 

9i59 

9-722 

998i 

21 

4o 

986762 

989442 

99l82O 

993897 

99567i 

997i4i 

9983o8 

999171 

999729 

9V9983 

2O 

4i 

6809 

9484 

i857 

3929 

5698 

7i63 

8325 

918: 

9736 

9985 

'9 

42 

6856 

9526 

i894 

396i 

5725 

7i85 

8342 

9194 

9743 

9986 

18 

43 

690? 

9568 

I93i 

3993 

5752 

7207 

8359 

92o6 

9749 

9988 

17 

44 

695o 

96io 

i968 

4oa5 

5778 

7229 

8375 

92l8 

9756 

9989 

16 

45 

6996 

965i 

2OO5 

4o56 

58o5 

725o 

8392 

9229 

9762 

999° 

i5 

46 

7o43 

9693 

2042 

4o88 

5832 

7272 

84o8 

9240 

9768 

9993 

i4 

47 

7090 

9735 

2078 

4l20 

5858 

7293 

8425 

9252 

9775 

•9993 

i3 

48 

7I36 

9776 

2Il5 

4i5i 

5884 

73i4 

844  1 

926^ 

978i 

9994 

12 

49 

7i83 

9818 

2l5l 

4182 

Sgii 

7336 

8457 

9274 

9787 

9995 

II 

5o 

987229 

989859 

992i87 

9942i4 

995937 

997357 

998473 

999285 

99979s 

979996 

10 

5i 

7275 

9900 

222<^ 

4a45 

5963 

7378 

8489 

9296 

9799 

9997 

9 

52 

7322 

9942 

226o 

4276 

5989 

7399 

85o5 

9307 

9804 

9997 

53 

7368 

9983 

2296 

43o7 

6oi5 

7420 

852i 

93i8 

9810 

9998 

7 

54 

74i4 

99002^ 

2332 

4338 

6o4i 

744i 

8537 

9328 

9816 

9998 

6 

55 

746o 

oo65 

2368 

4369 

6067 

7462 

855a 

9339 

9821 

9999 

5 

56 

75o6 

oio5 

24O2 

44oo 

6093 

7482 

8568 

935o 

9827 

9999 

4 

5 

755 

oi46 

243$ 

443c 

6118 

75ov 

8583 

936o 

9832 

1.  00000 

3 

58 

759 

0187 

247^ 

446 

6i44 

7523 

8599 

937° 

9837 

oooo 

• 

5 

764 

0228 

25ll 

44g 

6169 

7544 

86i4 

938 

9843 

0000 

i 

9° 

8° 

7° 

6° 

5° 

4° 

3° 

2° 

1° 

0° 

c 

Natural  Co-sines. 

i 

Jo'*;.0-80 

0.72 

o.63 

o.55 

0.46 

o.38 

o.3o 

O.2I 

o.i3 

o.o4 

NATURAL    TANGENTS. 


133 


j 

80°  1  81° 

82° 

83° 

84° 

85° 

86° 

87° 

88° 

89° 

0 

5.67128  6.3i375 

7.n537 

8.i4435 

9.5i436 

n.43oi 

i4«3oo7 

19.0811 

28.6363 

57.29oo 

60 

I 

8o94;   2566   3o42 

6398 

4io6 

4685 

36o7 

1879 

877i 

58.2612 

59 

2 

9064   3761 

455-3 

837o 

6791 

5o72 

4212 

2959 

29.1220 

59.2659 

58 

3 

5.70037!  4<?6i 

6071 

8.20352 

9490 

546  1 

4823 

4o5i 

.  37n 

6o.3o58 

57. 

4 

ioi3 

6i65 

7594 

2344 

0.  62205 

5853 

5438 

5i56 

6245 

6i.3829 

56 

5 

1992 

7374 

*  *  _ 
9125 

4345!  4935 

6248 

6o59 

6273 

8823 

62-4992 

55 

6 

2974 

8587 

7.20661 

6355 

7680 

6645 

6685 

74o3 

3o.i446 

63.6567 

54 

7 

3960 

9804 

22O4 

8376 

9.70441 

7045 

73i7 

8546 

4n6 

64.858o 

53 

8 

4949 

6.41026 

3754 

8.3o4o6 

32  17!   7448 

7954 

9702 

6833 

66.io55 

52 

9 

2253 

53io 

2446 

6009 

7853 

8596 

20.0872 

9599 

67.4oi9 

5i 

10 

5.76937 

6.43484 

7.26873 

8.34496 

9.78817 

11.8262 

14.9244 

2O.2O56 

3i.24i6 

68.75oi 

5o 

ii 

7936 

472O 

8442 

6555 

9.81641 

8673 

9898 

3253 

5284 

7o.i533 

49 

12 

8938 

596i 

7.3ooi8 

8625 

4482 

9087 

i5.o557 

4465 

82o5 

7i.6i5i 

48 

i3 

9944 

•7206 

1600 

8.4o7o5 

7338 

1222 

569i 

32.1181 

73.i39o 

47 

i4 

5.80953 

8456 

•3190 

2795 

9.9O2II 

9923 

i893 

6932 

42  1  3 

74-7292 

46 

i5 

1966 

9710 

4786 

4896 

3ioi 

I2.o346 

257I 

8188 

73o3 

76.39oo 

45 

16 

2982 

6.50970 

6389   7007 

6007 

0772 

3254 

946o 

33.o452 

78.i263 

44 

ll 

4ooi 

2234 

7999 

9128 

893i 

I2OI 

3943 

21.0747 

3662 

79.9434 

43 

18 

5024 

35o3 

9616 

8.5i259 

10.0187 

i632 

'  4638 

2049 

6935 

81.8470 

42 

J9 

6o5i 

4777 

7.41240 

3402 

o483 

2067 

534o 

3369 

34.0273 

83.8435 

4i 

20 

5.87080 

6.56o55 

7.42871 

8.55555 

10.0780 

I2.25o5 

i5.6o48 

21.4704 

34.3678 

85.9398 

4o 

21 

8n4 

7339 

4509 

77i8 

1080 

2946 

6762 

6o56 

7i5i 

88.1436 

39 

22 

9i5i 

862-7 

6i54 

9893 

i38i 

3390 

7483 

7426 

35.o695 

90.4633 

38 

23 

S.ooigi 

9921 

7806 

8.620-78 

i683 

3838 

8211 

88i3 

43i3 

92.9085 

37 

24 

!236 

6.61219 

9465 

4275 

i988 

4288 

8945 

22.0217 

8006 

95.4895 

36 

25 

2283 

2523 

7.5n32 

6482 

2294 

4742 

9687 

i64o 

36.i776 

98.2i79 

35 

26 

3335 

383i 

2806 

87oi 

2602 

5199 

i6.o435 

3o8i 

5627 

101.107 

34 

27 

439o 

5i44 

4487 

8.7o93i 

29l3 

566o 

II9O 

454i 

956o 

104.171 

33 

28 

5448 

6463 

6176 

3l72 

3224 

6124 

I952 

6020 

37.3579 

107.426 

32 

29 

65io 

7787 

7872 

5425 

3538;   659i 

2722 

75i9 

•7686 

IIO.892 

3i 

3o 

5.97576 

6.69116 

7.59575 

8.77689 

10.3854112.7062 

i6.3499 

22.9o38 

38.1885 

114.589 

3o 

3i 

8646 

6.7o45o 

7.61287 

9964 

4172 

7536 

4283 

23.o577 

6177 

118.540 

29 

32 

9720 

1789 

3oo5 

8.82252 

449i 

8oi4 

5o75 

2l37 

39.o568 

122.774 

28 

33 

6.00797 

3i33 

4732 

455i 

48i3 

8496 

5874 

37i8 

5o59 

I27.32I 

27 

34 

1878 

4483 

6466 

6862 

5i36 

8981 

6681 

532i 

9655 

132.219 

26 

35 

2962 

5838 

8208 

9i85 

5462 

9469 

7496 

6945 

4o.4358 

i37.5o7 

25 

36 

4o5i 

7199 

9957 

8.9i52o 

5789 

9962 

83i9 

8593 

91-74 

i43.237 

24 

37 

5i43 

8564 

7.7i7i5 

3867 

6118 

i3.o458 

9i5o 

24.0263 

4i.4io6 

149-465 

23 

38 

6240 

9936 

348o 

6227 

645o 

o958 

999° 

i957 

9i58 

i56.259 

22 

39 

734o 

6.8i3i2 

5254 

8598 

6783 

i46i 

I7.o837 

3675 

42.4335 

i63.7oo 

21 

4o 

6.o8444 

6.82694 

7.77o35 

9.oo983 

io.7n9 

i3.i969 

I7.i693 

24.54i8 

42.964i 

171.885 

20 

4i 

9552 

4082 

8825 

3379 

7457 

2480 

2558J   7i85 

43.5o8i 

180.932 

I9 

42 

6.io664 

5475 

•7.80622 

5789 

7797 

2996 

3432J   8978 

44.o66i 

190.984 

18 

43 

1779 

6874 

2428 

8211 

8139 

35i5 

43i4'25.o798 

6386 

202.219 

17 

44 

2899 

8278 

4242 

9.10646 

8483 

4039 

52o5|   2644 

45.2261 

2i4.858 

16 

45 

4oa3 

9688 

6o64 

3o93 

8829 

4566 

6106 

45i7 

8294 

229.182 

i5 

46 

5i5i 

6.9110^ 

7895 

5554 

9178 

5o98 

7oi5 

64i8 

46.4489 

245.552 

i4 

47 

6283 

2525 

9734 

8028 

9529 

5634 

7934 

8348 

47.o853 

264.441 

i3 

48 

74*9 

3952 

7.9i582 

9.2o5i0 

9882 

6174 

8863 

26.o3o7 

7395 

286.478 

12 

49 

8559 

5385 

3438 

3oi6 

11.0237 

67I9 

9802 

2296 

48.4i2i 

3I2.52I 

II 

5o 

6.i97o3 

6.96823 

7.953o2 

9.  2553o 

n.o594 

i3.7267 

i8.o75o 

26.43i6 

49.1039 

343.774 

IO 

5i 

6.2o85i 

8268 

7i76 

8o58 

o954 

•7821 

I7o8 

6367 

8i57 

381.9-71 

9 

5s 

2003 

9718 

9o58 

9.3o599 

i3i6 

8378 

2677 

845o 

5o.5485 

429.  -718 

8 

53 

3i6o 

7.01174 

8.oo948 

3i55 

1681 

894o 

3655 

27.o566 

5i.3o32 

491.106 

7 

54 

43ai 

2637 

2848 

572/j 

2048 

95o7 

4645 

27l5 

52.o8o7 

5-72.95-7 

6 

55 

5486 

4io5 

4756 

83o7 

2417 

i4-oo79 

56^5 

4899 

8821 

687.549 

5 

56 

6655 

5579 

6674 

9.4o9o4 

2789 

o655 

6656 

71*17 

53.7o86 

859.436 

4 

57 

7829 

7°^9 

8600 

35i5 

3i63 

1235 

7678 

9372 

54-56i3 

1145.92 

3 

58 

9oo7 

8546 

8.io536 

6i4i 

354o 

1821 

8711 

28.1662 

55.44i5 

1718.87 

2 

59 

6  30189 

7.ioo38 

2481 

878i 

39i9 

2411 

9755 

3994 

56.35o63437.75 

I 

9° 

8° 

7° 

6° 

5° 

4° 

3°    2° 

1°     0° 

A 

Natural  Co-tangents. 

,  •** 

P.  P.   go 

22.  IO 

28.^46 

37.83 

5.28 

7.88 

iS.oi 

1 

y 

<j  i  .  \j 

/  •  * 

NATURAL    SECANTS. 


Deg. 

0' 

10' 

20' 

30' 

.40' 

50' 

P.  Part 
tol'. 

0 

i  .000000 

i  .000004 

i  .000017 

i  ,oooo38 

i  .000068 

i  .000106 

89 

2.5 

I 

000l52 

000207 

000271 

ooo343 

000423 

ooo5i2 

88 

7.6 

2 

000609 

000715 

ooo83o 

ooogSS 

001084 

001224 

87 

I2.7 

3 

001372 

001529 

001695 

001869 

OO2o5l 

002242 

86 

I7.8 

£ 

002442 

oo265o 

002867 

003092 

oo3326 

003569 

85 

22.9 

5 

oo382o 

oo4o8o 

oo4348 

oo4625 

oo49n 

oo52o5 

84 

28.1 

6 

oo55o8 

.o582o 

oo6i4i 

oo647o 

006808 

007154 

83 

33.3 

7 

007510 

007874 

008247 

008629 

OO9O2O 

009419 

82 

38.6 

8 

009828 

010245 

r»  1671 

011106 

on55o 

012003 

81 

43.9 

9 

oi2465 

012936 

o.34i6 

oi39o5 

oi44o3 

014910 

80 

49.3 

10 

1.015427 

i  .015952 

i  .016487 

i  .oi7o3o 

i.oi7583 

I.  018145 

79 

54.8 

ii 

018717 

019297 

019887 

O2O487 

02I095 

021713 

78 

60.4 

12 

022341 

022977 

023624 

024280 

O24945 

O2562O 

77 

66.0 

i3 

0263o4 

026998 

027702 

O284i5 

029i38 

029871 

76 

71.8 

i4 

o3o6i4 

o3i366 

032128 

032900 

o33682 

034474 

75 

77-7 

i5 

035276 

o36o88 

036910 

o37742 

o38584 

039437 

74 

83.7 

16 

040299 

041172 

o42o55 

042949 

o43853 

044767 

73 

89.8 

17 

045692 

046627 

o47573 

048529 

o49496 

o5o474 

72 

96.1 

18 

o5i462 

o5246i 

o5347i 

054492 

o55524 

o56567 

71 

IO2.6 

'9 

057621 

o58686 

059762 

060849 

o6i947 

o63o57 

70 

109.2 

20 

1.064178 

i.o653io 

i.o66454 

i.o676o9 

i  .o68776 

1.069955 

69 

116.1 

21 

071145 

072347 

073561 

o74786 

0-76024 

077273 

68 

123.2 

22 

o78535 

079808 

081094 

082392 

o837o3 

o85o25 

67 

i3o.4 

23 

o8636o 

087708 

089068 

090441 

091827 

093225 

66 

137.9 

24 

o94636 

096060 

097498 

098948 

ioo4ii 

101888 

65 

145.6 

25 

io3378 

104881 

106398 

io7929 

109473 

ino3o 

64 

iS3.7 

26 

112602 

114187 

n5787 

117400 

i  19028 

120670 

63 

162.0 

27 

122326 

i23997 

125682 

I27382 

129096 

130826 

62 

170.7 

28 

132570 

i34329 

i36io4 

i37893 

139698 

i4i5i8 

61 

179.7 

29 

143354 

i452o5 

147073 

148956 

i5o854 

152769 

60 

189.1 

3o 

I.I5470I 

i.  i  56648 

i.i586i2 

i  .  160592 

1.162589 

I.i646o3 

59 

198.9 

3i 

166633 

168681 

170746 

1-72828 

17492-7 

177044 

58 

209,  i 

32 

179178 

i8i33i 

i835oi 

i85689 

i87895 

190120 

57 

219.7 

33 

192363 

i94625 

196906 

199205 

2Ol523 

2o386i 

56 

230.9 

34 

206218 

2o8594 

210991 

2i34o6 

2i5842 

218298 

55 

242.6 

35 

220775 

223271 

225789 

228327 

23o886 

233466 

54 

254.8 

36 

236o68 

23869i 

24i336 

244oo3 

246691 

249402 

53 

267.7 

37 

252i36 

254892 

257671 

26o472 

263298 

266146 

52 

281.3 

38 

269018 

27i9i4 

274834 

277779 

280748 

28374i 

5i 

295.6 

39 

286760 

2898o3 

292872 

295967 

299088 

302234 

5o 

310.7 

4o 

I.3o54o7 

i.  308607 

i.3n833 

i.3i5o87 

x.3i8368 

1.321677 

49 

326.7 

4i 

325oi3 

328378 

33i77i 

335i92 

338643 

342123 

48 

343.6 

42 

345633 

349i72 

352742 

356342 

359972 

363634 

47 

36i.5 

43 

367327 

37io52 

3748o9 

378598 

382420 

386275 

46 

38o.5 

44 

390164 

394o86 

398o42 

402032 

406057 

4iou8 

45 

400.7 

45   414214 

4i8345 

4225i3 

4267l8 

430960 

435239 

44 

422.3 

46   43g557 

4439i2 

4483o6 

45274o 

457213 

461-726 

43 

445.3 

47  :  466279 

470874 

4755o9 

48oi87 

484907 

4896-70 

42 

469.8 

48  i  494477 

499327 

5o422I 

509160 

5i4i45 

5i9i76 

4i 

496.2 

49  i   524253 

529377 

534540 

539-769 

545o38 

55o356 

4o 

524.4 

5o 

i  555724 

i.56n42 

i.5666i2 

i.572i34 

1.577708 

1.583335 

39 

554.7 

5i 

589016 

594751 

6oo542 

6o6388 

612291 

6i825i 

38 

587.4 

52 

624269 

63o346 

636483 

642680 

648938 

655258 

37 

622.7 

53 

66i64o 

668086 

674597 

68n73 

6878i5 

694524 

36 

660.9 

54 

701302 

708148 

7i5o64 

722051 

729110 

736244 

35 

702.2 

55 

C  /? 

743447 

750727 

758o84 

7655i7 

773029 

780620 

34 

747.2 

56 

788292 

796045 

8o388i 

811801 

819806 

827899 

33 

796.2 

r  o 

836o78 

844348 

8527o7 

861159 

869704 

878344 

32 

849.8 

58 
59 

887080 
94i6o4 

8959i4 
95io58 

9o4847 
960621 

9i388i 
970294 

923017 
980081 

932258 
989982 

3i 

3o 

908.5 
973.o 

60' 

50' 

40' 

30' 

20' 

10' 

Dr.  5. 

Natural  Co-secants. 

.NATURAL    SECANTS. 


135 


Deg. 

0' 

10' 

30' 

30' 

40' 

50' 

P.  Part 
tol'. 

60 

2.OOOOOO 

2.oioi36 

2.020393 

2.030772 

2.041276 

2.061906 

29 

io44 

6l 

062665 

073666 

084679 

096739 

107036 

118474 

28 

1123 

62 

i3oo54 

141781 

x53655 

166681 

177869 

190196 

27 

I2IO 

63 

202689 

2i5346 

228168 

241168 

264320 

267667 

26 

i3o8 

64 

281172 

294869 

308760 

322820 

337083 

35x542 

26 

1417 

65 

866202 

38io65 

396137 

4ix42i 

426922 

442645 

24 

i539 

66 

458593 

474773 

491187 

5o7843 

524744 

641896 

23 

1678 

67 

5593o5 

676976 

694914 

6x3x26 

53x6x8 

660396 

22 

i835 

68 

669467 

688387 

708614 

728604 

7488x4 

769453 

21 

20X5 

69 

790428 

811747 

8334x9 

85545i 

877853 

900635 

2O 

2222 

7C 

2.923804 

2.947372 

2.971349 

2.996744 

3.020669 

3.045835 

*9 

246l 

71 

3.o7i553 

3.097736 

3.124396 

3.i5x545 

179198 

207367 

18 

2740 

72 

236o68 

2653x5 

296123 

326610 

366490 

388082 

17 

3o68 

73 

42o3o4 

453i73 

486711 

620937 

556871 

59i536 

16 

3458 

74 

627955 

666162 

7o3i5x 

741978 

781660 

822226 

16 

3926 

75 

8637o3 

906126 

949622 

993929 

4.039380 

4.086913 

i.4 

4492 

76 

4.133565 

4.182378 

4.232394 

4.283658 

3362i5 

390116 

i3 

6190 

77 

4454n 

602167 

56o4o8 

620226 

681676 

74482i 

12 

6062 

78 

8o9734 

876491 

946169 

5.016862 

6.088628 

5.i63592 

II 

7171 

79 

5.  24o843 

5.320486 

5.402633 

487404 

674926 

665333 

10 

8612 

80 

5.758770 

5.855392 

5.955362 

6.068868 

6.  166067 

6.277193 

9 

81 

6.392453 

6.  612081 

6.636329 

6.766469 

6.899794 

7.039622 

8 

82 

7.185297 

7.337191 

7.496711 

7.661298 

7.834433 

8.016646 

7 

83 

8.206609 

8.404669 

8.613790 

8.833671 

9.o65x5i 

9.309170 

6 

84 

9.566772 

9.839123 

xo.  12762 

io.43343 

10.76849 

ii.io455 

5 

85 

11.47371 

xi.86837 

12.29126 

12.74549 

13.23472 

13.76311 

4 

86 

14.33559 

14.96788 

i5.63679 

x6.38o4x 

17.19843 

18.  10262 

3 

87 

19.10732 

20.23028 

21.49368 

22.92669 

24.66212 

26.46061 

2 

88 

28.65371 

31.26768 

34.38232 

38.20x55 

42.97671 

49.  n4o6 

I 

89 

57.29869 

68.76736 

86.94661 

114.6930 

171.8883 

343.7762 

0 

60' 

50' 

40' 

30' 

20' 

10' 

Deg. 

Natural  Co-secants. 

LENGTHS  OF  CIRCULAR  ARCS. 

Degrees. 

Minutes. 

Seconds. 

o 

o 

0 

/ 

H 

I 

!oi74533 

26 

.4537856 

5i 

.8901179 

I 

.0002909 

.ooooo48 

a 

.0349066 

27 

.4712389 

52 

.9076712 

2 

.0006818 

2 

.0000097  ' 

3 

.0623599 

28 

.4886922 

53 

.9260245 

3 

.0008727 

3 

.0000145 

4 

.0698132 

29 

.5o6i455 

54 

.9424778 

4 

.ooii636 

4 

.0000194 

5 

.0872665 

3o 

.5235988 

55 

.9699311 

5 

.0014544 

5 

.0000242 

6 

.1047198 

3x 

.5410621 

56 

•9773844 

6 

.0017453 

6 

.0000291 

7 

.  1221730 

32 

,5585o54 

57 

•9948377 

7 

.0020362 

7 

.OOO0339 

8 

.1396263 

33 

.6769687 

58 

.0122910 

8 

.0023271 

8 

.oooo388 

9 

.1670796 

34 

.6934119 

59 

.0297443 

9 

.0026180 

9 

.oooo436 

10 

.1745329 

35 

.6108662 

60 

.0471976 

10 

.0029089 

10 

,oooo485 

ii 

.  1919862 

36 

.6283x85 

65 

.  i  34464o 

ii 

.0031998 

ii 

.oooo533 

12 

.2094396 

37 

.6467718 

70 

.2217306 

12 

.0034907 

12 

.0000682 

i3 

.2268928 

38 

.6632261 

75 

.3089969 

x3 

.0037816 

i3 

.oooo63o 

i4 

.244346i 

39 

.6806784 

80 

.3962634 

i4 

.0040724 

i4 

.0000679 

i5 

.2617994 

4o 

.6981317 

85 

.4836299 

i5 

.oo43633 

16 

.0000727 

16 

.2792627 

4i 

.7x5585o 

9° 

.6707963 

16 

.0046642 

16 

.0000776 

17 

.2967060 

42 

.733o383 

100 

.7453293 

17 

.0049461 

ll 

.0000824 

18 

.3i4i593 

43 

.7604916 

1X0 

.9198622 

18 

.0062360 

18 

.0000873 

I9 

.33i6i26 

44 

.7679449 

I2O 

2.0943961 

J9 

.0066269 

J9 

.0000921 

20 

.  3490669 

45 

.7863982 

x3o 

2.2689280 

20 

.0068178 

20 

.0000970 

21 

.3665i9i 

46 

.8028616 

x4o 

2.4434610 

26 

.0072722 

26 

.0001212 

22 

.3839724 

47 

.82o3o47 

x5o 

2.6179989 

3o 

.0087266 

'>o 

.oooi454 

•3 

.4014267 

48 

.8377680 

1  60 

2.7926268 

4o 

.01x6355 

40 

.0001939 

24 

.4188790 

49 

.85521x3 

170 

2.9670697 

5o 

.0145444 

5o 

.0002424 

25 

.4363323 

5o 

-.8726646 

1  80 

3.1416927 

60 

.0174533 

60 

.0002909 

ISC) 


TRAVERSE    TABLE. 


Course. 

Dist.  I. 

Dist.  2. 

Dist.  3. 

Dist.  4. 

* 

Dist.  6. 

Lat 

Dep. 

Lat 

Dep. 

Lat 

Dep. 

Lat 

Dep. 

Lat 

Dep. 

o   / 

0     / 

o  i5 

I.OOOO 

c.  oo4/4 

?  OOOO 

o.oo87 

3.  oooo 

o.oiSi 

4-OOOO 

O.OI75 

5.  OOOO 

O.O2I$ 

89  45 

3o 

OOOO 

oo87 

1.9999 

oi75 

2.9999 

0262 

3.9998 

o349 

4-9998 

o436 

3o 

45 

0.9999 

oi3i 

9998 

0262 

9997 

o393 

9997 

o52^! 

9996 

o654 

i5 

I    O 

9998 

oi75 

9997 

o349 

9995 

o524 

9994 

o698 

9992 

087; 

89   o 

16 

9998 

0218 

1 

9995 

o436 

9993 

o654 

999° 

o873 

0988 

io9i 

45 

3o 

9997 

0262 

9993 

o524 

999° 

o785 

9986 

io47 

5983 

i3o9 

3o 

45 

r 

9995 

o3o5 

9991 

0611 

9986 

o9i6 

998i 

1222 

9977 

i527 

16 

2   0 

9994 

o349 

9988 

o698 

9982 

io47 

9976 

i396 

9970 

i745 

88   o 

i5 

9992 

o393 

9985 

o785 

9977 

1178 

9969 

i57o 

996i 

i963 

45 

3o 

9990 

o436 

998i 

o872 

997i 

i3o9 

9962 

i745 

9952 

2181 

3o 

45 

0.9988 

o.o48o 

i.9977 

o.o96o 

2.9966 

o.i439 

3.9954 

o.i9i9 

4*9942 

o.2399 

i5 

3   o 

9986 

o523 

9973 

io47 

9959 

i57o 

9945 

2093 

993i 

26l7 

87   o 

i5 

9984 

o567 

9968 

n34 

9952 

I7OI 

9936 

2268 

9920 

2835 

45 

3o 

9981 

0610 

9963 

1221 

9944 

i83i 

9925 

2442 

9907 

3o52 

3o 

45 

9979 

o654 

9957 

i3o8 

9936 

I962 

99i4 

2616 

9893 

3270 

i5 

4  o 

9976 

o698 

995i 

i395 

9927 

2093 

99o3 

279O 

9878 

3488 

86   o 

i5 

9973 

o74i 

9945 

1482 

9918 

2223 

989o 

2964 

9863 

37o* 

45 

3o 

9969 

o785 

9938 

i569 

99o8 

2354 

9877 

3i38 

9846 

3923 

3o 

45 

9966 

0828 

993i 

i656 

9897 

2484 

9863 

33i2 

9828 

4i4o 

i5 

5  o 

9962 

o872 

9924 

i743 

9886 

26i5 

9848 

3486 

98io 

4358 

85   o 

i5 

o.9958 

o.o9i5 

1.9916 

o.i83o 

2.9874 

o.2745 

3.9832 

o.366o 

4.979o 

o.4575 

45 

3o 

9954 

o958 

99o8 

I9i7 

9862 

2875 

98i6 

3834 

977° 

4792 

3o 

45 

995° 

1002 

9899 

2004 

9849 

3oo6 

9799 

4oo8 

9748 

5oo9 

i5 

6  o 

9945 

io45 

989o 

2O9I 

9836 

3i36 

978i 

4i8i 

9726 

5226 

84   o 

i5 

9941 

1089 

988i 

2I77 

9822 

3266 

9762 

4355 

97o3 

5443 

45 

3o 

9936 

iiSa 

987i 

2264 

98o7 

3396 

9743 

4528 

9679 

566o 

3o 

45 

993i 

n75 

986i 

235l 

9792 

3526 

9723 

47oi 

9653 

5877 

i5 

7  ° 

9925 

1219 

985i 

a437 

9776 

3656 

9702 

4875 

9627 

6o93 

83   o 

i5 

9920 

1262 

984o 

2524 

976o 

3786 

968o 

5o48 

9600 

63io 

45 

3o 

Q9i4 

i3o5 

9829 

2611 

9743 

39i6 

9658 

5221 

9572 

6526 

3o 

45 

0.9909 

0.1349 

i.98i7 

o.2697 

2.9726 

o.4o46 

3.9635 

o.5394 

4.9543 

o.6743 

i5 

8.  o 

9903 

1392 

98o5 

2783 

97o8 

4i75 

96n 

5567 

95i3 

6959 

82   o 

i5 

9897 

i435 

9793 

2870 

969o 

43o5 

9586 

574o 

9483 

7175 

45 

3o 

989o 

i478 

978o 

2956 

967o 

4434 

956i 

59I2 

945i 

739o 

3o 

45 

9884 

l52I 

9767 

3o42 

965i 

4564 

9534 

6o85 

94i8 

7606 

i5 

9  o 

9877 

1  564 

9754 

3i29 

963i 

4693 

95o8 

6257 

9384 

7822 

81   o 

i5 

987o 

i6o7 

974o 

32  1  5 

96io 

4822 

948o 

643o 

935o 

8037 

45 

3o 

9863 

i65o 

9726 

33oi 

9589 

495i 

945i 

6602 

93i4 

8252 

3o 

45 

9856 

i693 

97n 

3387 

9567 

5o8o 

9422 

6774 

9278 

8467 

i5 

10   0 

9848 

I736 

9696 

3473 

9544 

52O9 

9392 

6946 

9240 

8682 

80   o 

i5 

o.984o 

o-i779 

i.968i 

o.3559 

2.952I 

0.5338 

3.9362 

o.7n8 

[.9202 

o.8897 

45 

.  3o 

9833 

1822 

9665 

3645 

9498 

5467 

933o 

7289 

9i63 

9II2 

3o 

45 

9825 

i865 

9649 

373o 

9474 

5596 

9298 

746  1 

9I23 

9326 

i5 

II    0 

98i6 

1908 

9633 

38i6 

9449 

5724 

9265 

7632 

9o8i 

954o 

70   o 

i5 

98o8 

igSi 

96i6 

3902 

9424 

5853 

923l 

7804 

9o39 

9755 

45 

3o 

9799 

1994 

9598 

3987 

9398 

598i 

9197 

7975 

8996 

9968 

3o 

45 

979° 

2o36 

958i 

4o73 

937i 

6io9 

9l62 

8i46 

8952 

1.0182 

i5 

12   o 

978i 

ao79 

9563 

4i58 

9344 

6237 

9I26 

83i6 

89o7 

o396 

78   o 

i5 

9772 

2122 

9545 

4244 

93i7 

6365 

9o89 

8487 

8862 

o6o9 

45 

3o 

9763 

2  1  64 

9526 

4329 

9289 

6493 

9o52 

8658 

88i5 

0822 

3o 

45 

o.9753 

O.22O7 

i.95o7 

o.44  1  4 

2.926o 

0.6621 

3.9oi4 

0.8828 

4.8767 

i.io35 

i5 

i3  o 

9744 

2250 

9487 

4499 

923l 

6749 

8975 

8998 

87i9 

1248 

77   ° 

i5 

9734 

2292 

9468 

4584 

920I 

6876 

8935 

9i68 

8669 

i46o 

45 

3o 

9724 

2334 

9447 

4669 

9I7I 

7oo3 

8895 

9338 

8618 

l672 

3o 

45 

97i3 

2377 

9427 

4754 

9i4o 

7i3i 

8854 

95o7 

8567 

1884 

-5 

i4  o 

97o3 

2419 

94o6 

4838 

9I09 

7258 

8812 

9677 

85i5 

2O96 

76   o 

i5 

9692 

2462 

9385 

4923 

9°77 

7385 

8769 

9846 

8462 

a3o8 

45 

3o 

968i 

25o4 

9363 

5oo8 

9o44 

75n 

8726 

I.OOlS; 

8407 

25i9 

3o 

45 

967o 

2546 

934i 

5o92 

9OII 

7638 

8682 

0184 

8352 

273o 

i5 

i5  o 

9659 

2588 

93i9 

5i76 

8978 

7765 

8637 

o353 

8296 

294l 

75   o 

Dep. 

Lat 

Dep. 

Lat 

Dep. 

Lat 

Dep. 

Lat.  i 

Dep. 

Lat 

Dist.  1. 

Dist.  2. 

Dist.  3. 

Dist.  4.     Dist.  5. 

Couna. 

TRAVERSE    TABLE. 


137 


Course. 

Dist.  6. 

Dist,  7. 

Dist.  8. 

Dist.  9. 

Dist.  10. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat.  j  Dep. 

Lat  i 

Dep. 

Lat 

Dep. 

o   / 

0      / 

o  i5 

6.9999 

.0262 

•9999 

o.o3o5 

•9999 

o.o349 

•9999 

O.oSgS 

9-9999 

o.o436 

89  45 

3o 

9998 

o524 

9997 

06  1  1 

9997 

o698 

9997 

o785 

9996 

o873 

3o 

45 

9995 

o785 

9994 

0916 

9993 

io47 

9992 

1178 

999  T 

i3oo 

i5 

:   o 

9991 

1047 

9989 

1222 

9988 

i396 

9986 

i57i 

9985 

I7451 

89   o 

i5 

9986 

1  309 

9983 

l527 

9981 

i745 

9979 

1963 

9976 

2181 

45 

3o 

9979 

1571 

9976 

i832 

9973 

2094 

9969 

2356 

9966 

2618 

3o 

45 

9972 

i832 

9967 

2i38 

9963 

2443 

9958 

2748 

9953 

3o54 

i5 

2   0 

9963 

2094 

99  5  7 

2443 

995i 

2792 

9945 

3i4i 

9939 

349o 

8   o 

i5 

9954 

2356 

9946 

2748 

9938 

3i4i 

993i 

3533 

9923 

3926 

45 

3o 

9943 

2617 

9933 

3o53 

9924 

349o 

9914 

3926 

99o5 

4362 

3o 

45 

5.993i 

.2879 

.9919 

0.3358 

•99°8 

0.3838 

.9896 

o.43i8 

.9885 

0.4798 

i5 

3   o 

9918 

3i4o 

99o4 

3664 

989o 

4i87 

9877 

47io 

9863 

5234 

7   o 

i5 

9904 

3402 

9887 

3968 

987i 

4535 

9855 

5l02 

9839 

5669 

45 

3o 

9888 

3663 

9869 

4273 

985i 

4884 

9832 

5494 

98i3 

6io5 

3o 

45 

9872 

3924 

985o 

4578 

9829 

5232 

9807 

5886 

9786 

654o 

i5 

4  o 

9854 

4  1  85 

9829 

4883 

98o5 

558i 

9781 

6278 

9756 

6976 

6   o 

16 

9835 

444? 

9808 

5i88 

978o 

5929 

9753 

6670 

9725 

74n 

45 

3o 

9815 

4708 

9784 

5492 

9753 

6277 

9723 

7061 

9692 

7846 

3o 

45 

9794 

4968 

9760 

5797 

9725 

6625 

9691 

7453 

9657 

8281 

i5 

5   o 

9772 

5229 

9734 

6101 

9696 

6972 

9658 

7844 

96i9 

8716 

5   o 

i5 

5.9748 

.549o 

.9706 

o.64o5 

.9664 

0.7320 

.9622 

0.8235 

.958o 

o.9i5o 

45 

3o 

9724 

575i 

9678 

67O9 

9632 

7668 

9586 

8626 

954o 

9585 

3o 

45 

9698 

6on 

9648 

7013 

9597 

8oi5 

9547 

9017 

9497 

.0019 

i5 

6   o 

9671 

6272 

9617 

73i7 

9562 

8362 

95°7 

9408 

9452 

o453 

84  o 

i-5 

9643 

6532 

9584 

7621 

9525 

&709 

9465 

9798 

94o6 

0887 

45 

3o 

9614 

6792 

955o 

7924 

9486 

9o56 

942I 

.0188 

9357 

1320 

3o 

45 

9584 

7052 

95i5 

8228 

9445 

94o3 

9376 

0578 

93o7 

1754 

i5 

7   ° 

9553 

7312 

0478 

853i 

94o4 

975o 

9329 

0968 

9255 

2187 

83   o 

i5 

9520 

7572 

944o 

8834 

936o 

1.0096 

928o 

i358 

92OO 

2620 

45 

3o 

9487 

7832 

94oi 

9i37 

93i6 

o442 

923o 

1747 

9i44 

3o53 

3o 

45 

.9452 

o.8o9i 

.936i 

o.944o 

7.9269 

1.0788 

8.9i78 

1.2137 

9.9o87 

1.3485 

i5 

8   o 

94i6 

835o 

93r9 

9742 

9221 

n34 

91*4 

2526 

9027 

39i7 

82   o 

:5 

9379 

8610 

9276 

.0044 

9I72 

1479 

9o69 

2914 

8965 

4349 

45 

3o 

934i 

8869 

923l 

o347 

9I2I 

1825 

9OI  I 

33o3 

8902 

478i 

3o 

45 

9302 

9:27 

9i85 

o649 

9o69 

2170 

8953 

3691 

8836 

5212 

i5 

9   ° 

9261 

9386 

9i38 

o95o 

9oi5 

25i5 

8892 

4079 

8769 

5643 

81   o 

i5 

9220 

9645 

9o9o 

1262 

896o 

2859 

883o 

4467 

8700 

6o74 

45 

3o 

9177 

99o3 

9o4o 

i553 

89o3 

3204 

8766 

4854 

8629 

65o5 

3o 

45 

9i33 

1.0161 

8989 

i854 

8844 

3548 

8700 

524i 

8556 

6935 

i5 

IO   O 

9088 

o4i9 

8937 

2i55 

8785 

3892 

8633 

5628 

848  1 

7365 

80   o 

i5 

5.9042 

1.0677 

6.8883 

1.2456 

7.8723 

1.4235 

8.8564 

i.6oi5 

9.84o4 

1.7794 

45 

3o 

8995 

o93^ 

8828 

2756 

8660 

4579 

8493 

64oi 

8325 

8224 

3o 

45 

8947 

n9i 

8772 

3o57 

8596 

4922 

8421 

6787 

8245 

8652 

i5 

II    O 

8898 

i449 

8714 

3357 

853o 

5265 

8346 

7173 

8i63 

9o8i 

79   ° 

i5 

884? 

I7o5 

8655 

3656 

8463 

5607 

8271 

7558 

8079 

95o9 

45 

3o 

8795 

I962 

8595 

3956 

8394 

5949 

8i93 

7943 

7992 

9937 

3o 

45 

8743 

22I9 

8533 

4255 

8324 

629I 

8n4 

8328 

79°5 

2.o364 

i5 

12    O 

8689 

2475 

8470 

4554 

8252 

6633 

8o33 

8712 

78i5 

O79i 

78   o 

i5 

8634 

273l 

84o6 

4852 

8178 

6974 

795i 

9o96 

7723 

1218 

45 

3o 

8578 

2986 

834i 

5i5i 

8io4 

73i5 

7867 

948o 

763o 

1  644 

3o 

45 

5.852 

1.3242 

6.8274 

1.5449 

7.8027 

1.7656 

8.7781 

i.9863 

9.7534 

2.2070 

i5 

i3   o 

8462 

3497 

8206 

5747 

795o 

7996 

7693 

2.0246 

7437 

2495 

77   ° 

i5 

84o3 

3752 

8i37 

6o44 

7870 

8336 

760^ 

0628 

7338 

2920 

45 

3o 

8342 

4oo 

8o6e 

634 

779° 

8676 

75i3 

1010 

7237 

3345 

3o 

45 

828 

426 

799^ 

6638 

77°7 

9oi5 

742I 

I392 

7i34 

3769 

i5 

i4  o 

8218 

45i 

7921 

6935 

7624 

9354 

7327 

1773 

7o3o 

4l92 

76   o 

i5 

8i54 

4769 

784C 

723 

7538 

9692 

723l 

2i54 

6923 

46i5 

45 

3o 

8089 

502 

777c 

7527 

7452 

2.oo3o 

7i33 

2534 

68i5 

5o38 

3o 

45 

802^ 

627 

769: 

7822 

?364 

o368 

7o34 

29l4 

6705 

546o 

i5 

i5   o 

795 

552 

76if 

Six 

727^ 

0706 

6933 

3294 

6593 

5882 

75   o 

Dep. 

Lat. 

Dg». 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat 

Dist.  6. 

Dist.  7. 

Dist.  8. 

Dist.  9. 

Dist.  10. 

Course. 

138 


TRAVERSE    TABLE. 


Course 

Dist.  1. 

Dist.  2. 

Dist.  3. 

Dist.  4. 

Dist.  5. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat 

Dep. 

Lat. 

Dep. 

Lat 

Dep. 

o   / 

o    / 

i5  i 

o.964£ 

0.263 

I.9296 

0.526 

2.894 

o.789 

3.859i 

1.052 

4823 

i.3i5 

74  45 

3 

963e 

267 

9273 

534 

89o 

801 

854f 

o69 

Si8 

336 

3o 

4 

06-26 

271^ 

9249 

542 

8874 

8i4 

849£ 

o85 

812 

357 

i5 

16   o 

9613 

276 

9225 

55i 

8838 

826 

845c 

102 

806 

378 

74   o 

i 

9600 

279 

92OI 

559 

880 

839 

8402 

II9 

800 

399 

45 

3o 

9588 

284 

9:76 

568 

8765 

852 

8353 

i36 

794 

420 

3o 

4 

95?6 

288 

9i5i 

5764 

8727 

864 

83o3 

l52 

787 

44  1 

i5 

17   o 

9563 

2922 

9I26 

584 

8689 

877 

825a 

i69 

781 

46i 

73   o 

i5 

955o 

2965 

9ioo 

593 

865i 

889 

8201 

186 

775 

482 

45 

3o 

9537 

3oo7 

9074 

6oi/ 

8612 

9O2 

8i49 

202 

7686 

5o3 

3o 

45 

0.9524 

o.3o49 

i.9o48 

o.6o9 

2.8572 

o.9i4 

3.8o96 

1.219 

4.7620 

1.5243 

i5 

18   o 

95n 

3090 

9O2I 

6180 

8532 

927 

8042 

236 

7553 

545 

72    0 

i5 

9497 

3i32 

8994 

6263 

849i 

9395 

7988 

252 

7485 

5658 

45 

3o 

9483 

3i73 

8966 

6346 

845o 

95i9 

7933 

2692 

74i6 

5865 

3o 

45 

9469 

32i4 

8939 

6429 

84o8 

9643 

7877 

2858 

7347 

6072 

i5 

19  o 

9455 

3256 

89io 

65u 

8366 

9767 

7821 

3o23 

7276 

6278 

7I    0 

i5 

944i 

3297 

8882 

6594 

8323 

989i 

7764 

3i88 

7204 

6485 

45 

3o 

9426 

3338 

8853 

6676 

8270. 

1.0012 

7706 

3352 

7l32 

669o 

3o 

45 

9412 

3379 

8824 

6758 

8235 

oi38 

7647 

35i7 

7o59 

6896 

i5 

20   0 

9397 

3420 

8794 

684o 

8i9i 

0261 

7588 

368i 

6985 

7101 

7o   o 

i5 

o.9382 

i.346i 

i.8764 

O.6922 

2.8146 

i.o384 

3.7528 

1.3845 

i.69io 

i.73o6 

45 

3o 

9367 

35o2 

8733 

7OO; 

8100 

o5o6 

7467 

4oo8 

6834 

75io 

3o 

45 

935i 

3543 

87o3 

7086 

8o54 

o629 

74o5 

4i7s 

6757 

77i5 

i5 

21    0 

9336 

3584 

8672 

7167 

8007 

o75i 

7343 

4335 

6679 

79i8 

69   o 

i5 

9320 

3624 

864o 

7249 

796o 

0873 

7280 

4498 

6600 

8122 

45 

3o 

93o4 

3665 

8608 

733o 

79i3 

o995 

7217 

466o 

652i 

8325 

3o 

45 

9288 

3706 

8576 

74n 

7864 

1117 

7l52 

4822 

644o 

8528 

i5 

22   0 

9272 

3746 

8544 

7492 

7816 

1238 

7087 

4984 

6359 

873o 

68   o 

15 

9255 

3786 

85n 

7573 

7766 

i359 

7022 

5i46 

62-7-7 

8932 

45 

3o 

9239 

3827 

8478 

7654 

7716 

i48i 

6955 

53o7 

6r94 

9i34 

3o 

45 

0.9222 

o.3867 

1.8444 

o.7734 

3.7666 

1.1601 

3.6888 

1.5468 

4-6i  10 

.9336 

i5 

23   0 

9205 

3907 

84io 

7816 

76i5 

1722 

6820 

5629 

6o25 

9537 

67   o 

i5 

9188 

3947 

8376 

7895 

7564 

1842 

6762 

579o 

594o 

9737 

45 

3o 

9171 

3987 

834i 

7975 

75l2 

I962 

6682 

595o 

5853 

9937 

3o 

4^ 

9i53 

4027 

83o6 

8o55 

7459 

2082 

6612 

6110 

5766 

2.0l37 

i5 

,24  o 

9i35 

4o67 

827I 

8i35 

74o6 

22O2 

6542 

6269 

5677 

o337 

66   o 

i5 

9118 

4107 

8235 

8214 

7353 

2322 

6470 

6429 

5588 

o536 

45 

3o 

9100 

4i4? 

8i99 

8294 

7299 

244  1 

6398 

6588 

5498 

o735 

3o 

45 

9081 

4i87 

8i63 

8373 

7244 

256o 

6326 

6746 

54o7 

o933 

i5 

25   0 

9063 

4226 

8126 

8452 

7i89 

2679 

6252 

6905 

53i5 

u3i 

65   o 

i5 

0.9045 

0.4266 

.8o89 

o.853i 

•7i34 

•2797 

.6178 

i.7o63 

.5223 

.1328 

45 

3o 

9026 

43o5 

8o52 

8610 

7o78 

29l5 

6io3 

722O 

5l29 

i526 

3o 

45 

9007 

4344 

8oi4 

8689 

•7021 

3o33 

6028 

7378 

5o35 

I722 

i5 

26  o 

8988 

4384 

7976 

8767 

6964 

3i5i 

5952 

7535 

494o 

I9I9 

64   o 

i5 

8969 

4423 

7937 

8846 

69o6 

3269 

5875 

-7692 

4844 

2Il4 

45 

3o 

8949 

4462 

7899 

8924 

6848 

3386 

5797 

7848 

4747 

23lO 

3o 

45 

8930 

45oi 

786o 

9002 

6789 

35o3 

57i9 

8oo4 

4649 

25o5 

i5 

27  o 

8910 

454o 

7820 

9080 

673o 

3620 

564o 

8160 

455o 

37OO 

3   o 

i5 

8890 

4579 

778o 

9i57 

6671 

3736 

556i 

83i5 

445i 

a894 

45 

3o 

8870 

46i7 

774o 

9235 

6610 

3852 

548o 

847o 

435i 

3o87 

3o 

45 

.885o 

0.4656 

.7700 

.9312 

.655o 

.3968 

.54oo 

1.8625 

•4a49 

.328i 

i5 

28   o 

8829 

4695 

7659 

9389 

6488 

4o84 

53i8 

8779 

4i47 

3474 

)2    O 

i5 

8809 

4733 

7618 

9466 

6427 

4200 

5236 

8933 

4o45 

3666 

45 

3o 

8788 

4772 

7576 

9543 

6365 

43i5 

5i53 

9o86 

394i 

3858 

3o 

45 

8767 

48io 

7535 

9620 

63o2 

443o 

5  069 

924o 

3836 

4o49 

i5 

39   o 

8746 

4848 

749a 

9696 

6239 

4544 

4985 

9392 

373i 

4a4o 

I    O 

i5 

87a5 

4886 

745o 

9772 

6i75 

4659 

49oo 

9545 

36a5 

443i 

45 

3o 

8704 

4924 

74o7 

9848 

6111 

4773 

48i4 

9697 

35i8 

4621 

3o 

45 

868a 

496a 

7364 

9924 

6o46 

4886 

4728 

9849i 

34io 

48ii 

i5 

3o   o 

8660 

5ooo 

732I 

c.oooo 

598i 

5ooo 

464  1 

.0000 

33oi 

5ooo 

0    O 

Dop. 

Lat 

Dep. 

Lat. 

Dep.  j  Lat 

Dep. 

Lat 

Dep. 

Lat  1 

Dist.  1. 

Dist.  2. 



Dist.  3. 

Dist.  4. 

Dist.  5. 

ourae. 

TRAVERSE    TABLE. 


Course. 

Dist.  6. 

Dist.  7. 

Dist.  8. 

Dist.  9. 

Dist.  10. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat 

Dep. 

o   / 

o    / 

i5  16 

5.7887 

1.5782 

6.7535 

i.84i2 

7.7i83 

2.IO42 

8.683i 

2.3673 

9.6479 

2.6303 

74  45 

3o 

7818 

6o34 

7454 

87o7 

7o9o 

i379 

6727 

4o5i 

6363 

6724 

3o 

45 

7?4? 

6286 

7372 

9ooi 

6996 

I7i5 

6621 

443o 

6246 

7i44 

r5 

16   o 

7676 

6538 

•7288 

9295 

69oi 

2o5i 

65i4 

48o7 

6126 

7564 

74  o 

i5 

7603 

6790 

72o3 

9588 

68o4 

2386 

64o4 

5i85 

6oo5 

7983 

45 

3o 

7529 

7o4i 

7117 

988i 

67o6 

272I 

6294 

556i 

5882 

8402 

3o 

45 

7454 

7292 

7o3o 

2.0I74 

6606 

3o56 

6181 

5938 

5757 

8820 

i5 

17   o 

7378 

7542 

694i 

o466 

65o4 

339o 

6o67 

63i3 

563o 

9237 

73   o 

T  *5 

73oi 

7792 

'  685i 

o758 

6402 

3723 

5952 

6689 

55o2 

9654 

45 

3o 

7223 

8042 

676o 

io49 

6297 

4o56 

5835 

7o64 

5372 

3.oo7i 

3o 

45 

5.7i44 

1.8292 

6.6668 

2.i34i 

7.6192 

2.4389 

8.57i6 

2.7438 

9.524o 

3.o486 

i5 

18   o 

7063 

854i 

6574 

i63i 

6o85 

472I 

SSgS 

78l2 

5io6 

O9O2 

72    0 

i5 

6982 

8790 

6479 

1921 

5976 

5o53 

5473 

8i85 

497o 

i3i6 

45 

3o 

6899 

9o38 

6383 

2211 

5866 

5384 

5349 

8557 

4832 

i73o 

3o 

45 

6816 

9286 

6285 

2501 

5754 

57i5 

5224 

893o 

4693 

2i44 

i5 

19   o 

673i 

9534 

6186 

2790 

564i 

6o45 

5o97 

93oi 

4552 

2557 

7I    0 

i5 

6645 

9781 

6086 

3o78 

5527 

6375 

4968 

9672 

44o9 

2969 

45 

3o 

6558 

2.0028 

5985 

3366 

54n 

67o5 

4838 

3.oo43 

4264 

338i 

3o 

45 

6471 

0275 

5882 

3654 

5294 

7o33 

47o6 

o4i3 

4n8 

3792 

i5 

20   o 

6382 

O52I 

5778 

3941 

5i75 

7362 

4572 

0-782 

3969 

4202 

7o   o 

i5 

5.6291 

2.0767 

6.5673 

2.4228 

7.5o55 

2.7689 

8.4437 

3.ii5i 

9.38i9 

3.46i2 

45 

3o 

6200 

1012 

5567 

45i5 

4934 

8oi7 

43oo 

i5i9 

3667 

5021 

3o 

45 

6108 

1257 

5459 

48oo 

48n 

8343 

4162 

1886 

35i4 

5429 

i5 

il    0 

6oi5 

i5o2 

535i 

5o86 

4686 

8669 

4022 

2253 

3358 

5837 

60   o 

i5 

5920 

1746 

5  24  1 

537i 

456i 

8995 

388i 

2619 

3201 

6244 

45 

3o 

5825 

1990 

5l29 

5655 

4433 

9320 

3738 

2985 

3o42 

665o 

3o 

45 

5729 

2233 

5oi7 

5939 

43o5 

9645 

SSgS 

335o 

2881 

7o56 

16 

22    O 

563i 

2476 

49o3 

6222 

4i75 

9969 

3447 

37i5 

27l8 

746i 

68   o 

15 

5532 

2719 

4788 

65o5 

4o43 

3.O292 

3299 

4o78 

2554 

7865 

45 

3o 

5433 

2961 

4672 

6788 

39io 

o6i5 

3i49 

4442 

2388 

8268 

3o 

45 

5.5332 

2.3203 

6.4554 

2.7070 

7.3776 

3.o937 

8.2998 

3.48o4 

9.222O 

3.867i 

i5 

23    0 

523o 

3444 

4435 

735i 

364o 

1258 

2845 

5i66 

2o5o 

9°73 

57   o 

i5 

5127 

3685 

43i5 

7632 

35o3 

i58o 

269I 

5527 

i879 

9474 

45 

3o 

5o24 

3925 

4i94 

79I2 

3365 

I900 

2535 

5887 

1-706 

9875 

3o 

45 

4919 

4i65 

4o72 

8l92 

3225 

222O 

2378 

6247 

i53i 

4.o275 

i5 

24   o 

48i3 

44o4 

3948 

84-72 

3o84 

2539 

22I9 

6606 

i355 

o674 

66   o 

i5 

4706 

4643 

3823 

875o 

294i 

2858 

2o59 

6965 

11-76 

I072 

45 

3o 

4598 

4882 

3697 

9029 

2797 

3i75 

i897 

7322 

o996 

i469 

3o 

45 

4489 

5l20 

357o 

93o6 

265i 

3493 

:733 

7679 

o8i4 

1866 

i5 

25    0 

4378 

5357 

3442 

9583 

25o5 

38o9 

i568 

8o36 

o63i 

2262 

65   o 

i5 

5.4267 

2.5594 

6.3312 

2.986o 

7.2356 

3.4i25 

8.i4oi 

3.839i 

9.o446 

4.2657 

45 

3o 

4i55 

583i 

3i8i 

3.oi36 

2207 

444  1 

1233 

8746 

O259 

3o5i 

3o 

45 

4042 

6067 

3o49 

o4u 

2o56 

4756 

io63 

9100 

OO7O 

3445 

i5 

26   o 

3928 

63o2 

29l6 

0686 

i9o4 

5o7o 

o89i 

9453 

8.9879 

3837 

64  o 

i5 

38i2 

6537 

278l 

o96o 

i75o 

5383 

o7i9 

9806 

9687 

4229 

45 

3o 

3696 

6772 

2645 

1234 

i595 

5696 

o544 

4-oi58 

9493 

462O 

3o 

45 

3579 

7006 

25o9 

i5o7 

i438 

6008 

o368 

0509 

9298 

5oio 

i5 

27  o 

346o 

7239 

2370 

1779 

1281 

63i9 

OI9I 

0859 

9IOI 

5399 

63   o 

i5 

334i 

7472 

223l 

2o5i 

II2I 

663o 

OOI2 

1209 

89O2 

5787 

45 

3o 

3221 

7705 

209I 

2322 

o96i 

694o 

7.983i 

i557 

87oi 

6i75 

3o 

45 

5.3o99 

a.7937 

6.i949 

3.2593 

7-°799 

3.7249 

7.9649 

4.1905 

8.8499 

4.656i 

i5 

28  o 

2977 

8168 

1806 

2863 

o636 

7558 

9465 

2252 

8295 

6947 

62   o 

i5 

2853 

8399 

1662 

3i32 

o47i 

7866 

928o 

2599 

8o89 

7332 

45 

3o 

2729 

863o 

i5i7 

34oi 

o3o5 

8i73 

9o94 

2944 

788a 

77i6 

3o 

45 

2604 

8859 

i37i 

3669 

oi38 

8479 

89o5 

3289 

7673 

8o99 

i5 

20   O 

24?7 

9089 

1223 

3937 

6.997o 

8785 

87i6 

3633 

7462 

848  1 

61   o 

15 

235o 

93i7 

io75 

4203 

98oo 

9090 

8525 

3976 

7a5o 

8862 

45 

3o 

2221 

9545 

O925 

447o 

9628 

9394 

8332 

43i8 

7o36 

9242 

3o 

45 

2092 

9773 

o774 

4735 

9456 

9697 

8i38 

4659 

6820 

9622 

i5 

3o   o 

1962 

3.0000 

0622 

5ooo 

9282 

4.0000 

7942 

5ooo 

66o3 

5.0000 

60   o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat 

Dist.  6. 

Dist.  7. 

Dist.  8. 

Dist.  9. 

Dist.  10. 

Course. 

?40 


TRAVERSE    TABLE. 


Course. 

Dist.  I. 

Dist.  2. 

Dist.  3. 

Dist.  4. 

Dist.  5. 

Lat. 

Dep. 

Lat 

Dep. 

Lat 

Dep. 

Lat 

Dep. 

Lat 

Dep. 

o   / 

3o  i5 

0.8638 

o.5o38 

1.7277 

i.oo75 

2.59l5 

I.5ll3 

3.4553 

2.Ol5l 

4.3192 

2.5l89 

o    / 

59  45 

3o 

8616 

5o75 

7233 

oi5i 

5849 

5226 

4465 

0302 

3o8i 

5377 

3o 

45 

8594 

5n3 

7l88 

0226 

5782 

5339 

4376 

0452 

2970 

5565 

i5 

3i   o 

8572 

5i5o 

ai43 

o3oi 

57i5 

545i 

4287 

0602 

2858 

5752 

59   o 

i5 

8549 

5i88 

7098 

o375 

5647 

5563 

4i96 

o75i 

2746 

5939 

45 

3o 

8526 

6226 

7o53 

o45o 

5579 

5675 

4io6 

o9oo 

2632 

6i25 

3o 

45 

85o4 

6262 

7007 

o524 

55u 

5786 

4oi4 

io49 

25i8 

63u 

i5 

32   0 

848o 

5299 

6961 

0598 

544  1 

5898 

3922 

H97 

2402 

6496 

58   o 

i5 

845y 

5336 

6916 

o672 

5372 

6008 

3829 

1  345 

2286 

6681 

45 

3o 

8434 

5373 

6868 

o746 

53o2 

6u9 

3736 

1492 

2I7O 

6865 

3o 

45 

o.84io 

o.54io 

1.6821 

1.0819 

2.5231 

1.6229 

3.3642 

2.1639 

4.2O52 

2.7o49 

i5 

33  o 

8387 

5446 

6773 

0893 

5i6o 

6339 

3547 

i786 

1934 

7232 

57   o 

i5 

8363 

5483 

6726 

0966 

5o89 

6449 

345i 

1932 

1814 

74i5 

45 

3o 

8339 

55i9 

66  78 

1039 

5oi7 

6558 

3355 

2077 

1694 

7597 

3o 

45 

83i5 

5556 

6629 

i  ii  i 

4944 

6667 

3259 

2223 

i573 

7779 

ID 

34  o 

8290 

6692 

658i 

1184 

487i 

6776 

3i62 

2368 

1452 

796o 

56   o 

i5 

8266 

5628 

6532 

1256 

4798 

6884 

3o64 

25l2 

i329 

8i4o 

45 

3o 

8241 

5664 

6483 

i328 

4724 

6992 

2965 

2656 

1206 

8320 

3o 

45 

8216 

5700 

6433 

i4oo 

4649 

7100 

2866 

2800 

1082 

85oo 

i5 

35   o 

8192 

5736 

6383 

1472 

4575 

7207 

2766 

2943 

o958 

8679 

55   o 

i5 

0.8x66 

0.5771 

1.6333 

i.i543 

2.4499 

i.73i4 

3.2666 

2.3o86 

4.o832 

2.8857 

45 

3o 

8i4i 

5807 

6282 

1614 

4423 

7421 

2565 

3228 

o7o6 

9o35 

3o 

45 

8116 

5842 

623i 

i685 

4347 

7527 

2463 

337o 

o579 

9212 

i5 

36  o 

8090 

5878 

6180 

i756 

427I 

7634 

236i 

35n 

o45i 

9389 

54   o 

i5 

8o64 

59i3 

6l29 

1826 

4i93 

7739 

2258 

3652 

0322 

9565 

45 

3o 

SoSg 

5948 

6o77 

1896 

4n6 

7845 

2l54 

3793 

0193 

974i 

3o 

45 

8oi3 

5983 

6026 

1966 

4o38 

795o 

2o5o 

3933 

oo63 

99i6 

i5 

3y  o 

7986 

6018 

5973 

2o36 

3959 

8o54 

1945 

4o73 

3.9932 

3.oo9i 

53   o 

i5 

7960 

6o53 

5920 

2106 

388o 

8i59 

i84o 

4212 

9800 

0265 

45 

3o 

7934 

6088 

5867 

2I75 

38oi 

8263 

1734 

435o 

9668 

o438 

3o 

45 

0.7907 

0.6122 

i.58i4 

1.2244 

2.372I 

i.8367 

3.1628 

2.4489 

3.9534 

3.o6i  i 

i5 

38  o 

7880 

6i57 

6760 

23i3 

364o 

8470 

l520 

4626 

94oi 

o783 

52    0 

i5 

7853 

6191 

57o6 

2382 

356o 

8573 

i4i3 

4764 

9266 

o955 

45 

3o 

7826 

6226 

6662 

245o 

3478 

8675 

i3o4 

49oi 

9i3o 

1  126 

3o 

45 

7799 

6259 

5598 

25i8 

3397 

8778 

irgS 

5o37 

8994 

I296 

i5 

3o   o 

7771 

6293 

5543 

2586 

33i4 

8880 

1086 

5i73 

8857 

f466 

5i   o 

i5 

.  7744 

6327 

5488 

2654 

3232 

898i 

0976 

53o8 

8720 

i635 

45 

3o 

7716 

636i 

5432 

2722 

3i49 

9o82 

o865 

5443 

858i 

1804 

3o 

45 

7688 

6394 

5377 

2789 

3o65 

9i83 

o754 

5578 

8442 

19-72 

i5 

4o  o 

7660 

6428 

532i 

2856 

298l 

9284 

0642 

57I2 

83o2 

2139 

5o   o 

i5 

0.7632 

o.646i 

i.5265 

1.2922 

2.2897 

i.9384 

3.o529 

a  5845 

3.8162 

3.23o6 

45 

3o 

7604 

6494 

52o8 

2989 

2812 

9483 

o4i6 

S978 

8020 

2472 

3o 

45 

7576 

6528 

5i5i 

3o55 

2727 

9583 

o3o3 

Oi  10 

7878 

2638 

i5 

4i  o 

7547 

656i 

5094 

3l2I 

2641 

9682 

0188 

6242 

7735 

28o3 

49  o 

i5 

75x8 

6593 

5o37 

3i87 

2555 

9780 

0074 

6374 

7592 

296-7 

45 

3o 

7490 

6626 

4979 

3252 

2469 

9879 

2.9958 

65o5 

7448 

3i3i 

3o 

45 

746  1 

665g 

4921 

33i8 

2382 

9976 

9842 

6635 

73o3 

3294 

i5 

4a   o 

743i 

6691 

4863 

3383 

2294 

2.0074 

9726 

6765 

7i57 

3457 

48   o 

i5 

7402 

6724 

48o4 

3447 

22O7 

0171 

9609 

6895 

7OI  I 

36i8 

45 

3o 

7373 

6756 

4746 

35i2 

2118 

0268 

9491 

•7024 

6864 

378o 

3o 

45 

0.7343 

0.6788 

1.4686 

i.3576 

2.2030 

2.o364 

2.9373 

2.7l52 

3.67i6 

3.394o 

i5 

43  o 

73i4 

6820 

462-7 

364o 

I94l 

o46o 

9254 

7280 

6568 

4ioo 

47   o 

i5 

7284 

6852 

4567 

37o4 

i85i 

o555 

9i35 

74o7 

64i9 

4259 

45 

3o 

7254 

6884 

45o7 

3767 

1761 

o65i 

9oi5 

7534 

6a69 

44i8 

3o 

45 

7224 

6916 

4447 

383o 

1671 

o745 

8895 

•7661 

6n8 

4576 

i5 

44  o 

7i93 

6947 

4387 

3893 

i58o 

o84o 

8774 

7786 

5967 

4733 

46   o 

i5 

7i63 

6978 

4326 

3956 

i489 

o934 

8652 

7912 

58i5 

489o 

45 

3o 

7i33 

7009 

4265 

4oi8 

i398 

IO27 

853o 

8o36 

5663 

5o45 

3o 

45 

7102 

7040 

4204 

4o8o 

i3o6 

II2O 

84o7 

8161 

55o9 

52OI 

:5 

45  o 

7071 

7071 

4i42 

4i42 

I2l3 

I2l3 

8284 

8284 

5355 

5355 

45   o 

Dep. 

Lat 

Dep. 

Lat. 

Dep. 

Lat 

Dep. 

Lat.  | 

Dep. 

Lat 

Dist.  1. 

Dist.  2. 

Dist.  3. 

Dist  4. 

Dist.  5. 

Course. 

TRAVERSE     IABLE. 


14 


Course. 

Dist.  6. 

Dist.  7. 

Dist.  8. 

Dist.  9. 

Dist.  10. 

Lat. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lot. 

Dep. 

o   / 

o    / 

3o  i5 

5.i83o 

3.0226 

6.o468 

3.5264 

6.9107 

4.0302 

7.7745 

4.5340 

8.6384 

5.0377 

59  45 

3o 

1698 

o452 

o3i4 

5528 

893o 

o6o3 

7547 

5678 

6i63 

o754 

3o 

45 

1  564 

0678 

oi58 

5791 

8753 

0903 

7347 

6016 

594i 

1129 

i5 

3i   o 

i43o 

09O2 

OOO2 

6o53 

8573 

1203 

7145 

6353 

57i7 

i5o^ 

59   o 

i5 

I295 

1126 

5.9844 

63i4 

839? 

i5o2 

6942 

6690 

5491 

i877 

45 

3o 

n58 

i35o 

9685 

6575 

8211 

1800 

6738 

7O25 

5264 

2250 

3o 

45 

1  02  1 

i573 

9525 

6835 

8028 

2097 

653a 

7359 

5o35 

2621 

i5 

32    0 

o883 

I795 

9363 

7094 

7844 

2394 

6324 

7693 

48o5 

2992 

58   o 

i5 

oy44 

2017 

9201 

7353 

7658 

2689 

6116 

8o25 

4573 

336i 

45 

3o 

o6o3 

2238 

9o37 

7611 

7471 

2984 

59o5 

8357 

4339 

373o 

3o 

45 

5.o462 

3.2458 

5.8873 

3.7868 

6.7283 

4.3278 

7.5694 

4.8688 

8.4io4 

5.409-7 

i5 

33   o 

0320 

2678 

87o7 

8i25 

7094 

3571 

548o 

9018 

3867 

4464 

57   o 

i5 

01-77 

2898 

854o 

838i 

6903 

3863 

5266 

9346 

3629 

4829 

45 

3o 

oo33 

3n6 

8372 

8636 

6711 

4i55 

5o5o 

9674 

3389 

5i94 

3o 

45 

4.9888 

3334 

8203 

8890 

65i8 

4446 

4832 

S.oooi 

3i47 

5557 

i5 

34   o 

9742 

3552 

8o33 

9144 

6323 

4?35 

46i3 

0327 

2904 

59i9 

56   o 

i5 

9595 

3768 

7861 

9396 

6127 

5o24 

4393 

o652 

2659 

6280 

45 

3o 

9448 

3984 

7689 

9648 

593o 

53i2 

4i7i 

°977 

a4i3 

664i 

3o 

45 

9299 

4200 

75i5 

99oo 

5732 

56oo 

3948 

i3oo 

2i65 

•7000 

i5 

35  o 

9149 

44i5 

734i 

4.oi5o 

5532 

5886 

3724 

1622 

igiS 

7358 

55   o 

i5 

4.8998 

3.4629 

5.7i65 

4.o4oo 

6.533i 

4.6172 

7.3498 

5.1943 

8.i664 

5.77i5 

45 

3o 

884? 

4842 

6988 

o649 

5129 

6456 

3270 

2263 

1412 

8070 

3o 

45 

8694 

5o55 

6810 

o897 

4926 

6740 

3o42 

2582 

n57 

8425 

i5 

36  o 

854i 

5267 

663: 

ii45 

4721 

7023 

2812 

2901 

0902 

8779 

54   o 

i5 

8387 

5479 

645  1 

l392 

45i6 

73o5 

258o 

32i8 

o644 

9i3i 

45 

3o 

823i 

5689 

6270 

i638 

43o9 

7586 

2347 

3534 

p386 

9482 

3o 

45 

8o75 

5899 

6088 

i883 

4ioo 

•7866 

2Il3 

3849 

OI25 

9832 

i5 

37  o 

7918 

6io9 

5904 

2I27 

389i 

8i45 

1877 

4i63 

-7.9864 

6.0182 

53   o 

i5 

7760 

63i8 

5720 

237I 

368o 

8424 

i64o 

4476 

9600 

0529 

45 

3o 

7601 

6526 

5535 

26i3 

3468 

87oi 

1402 

4789 

9335 

0876 

3o 

45 

4-?44i 

3.6733 

5.5348 

4.2855 

6.3255 

4.8977 

7.1162 

5.5ioo 

7^.9069 

6.1222 

i5 

38   o 

7281 

694o 

5i6i 

3o96 

3o4i 

9253 

092I 

54io 

8801 

1  566 

52    0 

i5 

7119 

7i46 

4972 

3337 

2825 

9528 

o679 

5718 

8532 

1909 

45 

3o 

6g56 

735i 

4?83 

3576 

26o9 

9801 

0435 

6026 

8261 

225l 

3o 

45 

6793 

7555 

4592 

38i5 

239I 

5.oo74 

oi9o 

6333 

7988 

2592 

i5 

3o   o 

6629 

7759 

44oo 

4o52 

2172 

o346 

6.9943 

6639 

77i5 

2932 

5i   o 

i5 

6464 

7962 

4207 

4289 

i95i 

0616 

9695 

6943 

7439 

327» 

45 

3o 

6297 

8i65 

4oi4 

4525 

1730 

0886 

9446 

7247 

•7162 

36o8 

3o 

45 

6i3i 

8366 

3819 

476i 

i5o7 

n55 

9196 

755o 

6884 

3944 

i5 

4o  o 

5963 

8567 

3623 

4995 

1284 

1423 

8944 

785i 

66o4 

4279 

5o   o 

i5 

4.5794 

3.8767 

5.3426 

4.5229 

6.1059 

5.1690 

6.8691 

5.8i5i 

7.6323 

6.4612 

45 

3o 

5624 

8967 

3228 

546  1 

o832 

1956 

8437 

845o 

6o4i 

4945 

3o 

45 

5454 

9i66 

3o3o 

5693 

o6o5 

2221 

8181 

8748 

5756 

5276 

i5 

4i  o 

5283 

9364 

283o 

5924 

o377 

2485 

7924 

9045 

547i 

56o6 

49   o 

i5 

5uo 

956i 

2629 

6i54 

0147 

2  748 

7666 

934i 

5i84 

5935 

45 

3o 

4937 

9757 

2427 

6383 

5.9916 

3oio 

7406 

9636 

4896 

6262 

3o 

45 

4763 

9953 

2224 

6612 

9686 

3271 

7i45 

9929 

46o6 

6588 

i5 

42   0 

4589 

4.oi48 

2O2O 

6839 

,9452 

353o 

6883 

6.O222 

43i4 

6913 

48   o 

i5 

44i3 

o342 

i8i5 

7066 

9217 

3789 

6620 

o5i3 

4022 

7237 

45 

3o 

4237 

o535 

1609 

7291 

8982 

4o47 

6355 

o8o3 

3728 

7559 

3o 

45 

44o59 

4.0728 

5.i4o3 

4.75.16 

5.8746 

5.43o4 

6.6089 

6.1092 

7.3432 

6.788o 

i5 

43  o 

388i 

O92O 

1195 

774o 

85o8 

456o 

5822 

i38o 

3i35 

8200 

47  o 

i5 

3702 

IIII 

0986 

79)53 

8270 

48i5 

5553 

1666 

2837 

85i8 

45 

3o 

3522 

i3oi 

o776 

8i85 

8o3o 

5o68 

5284 

1952 

2537 

8835 

3o 

45 

3342 

i49i 

o565 

84o6 

7789 

532i 

5oi3 

2236 

2236 

9i5i 

i5 

44  o 

3i6o 

1680 

o354 

8626 

7547 

5573 

474i 

2519 

i934 

9466 

46  o 

i5 

2978 

1867 

oi4i 

8845 

?3o4 

5823 

4467 

2801 

i63o 

9779 

45 

3o 

2795 

2o55 

4.9928 

9064 

7o6o 

6o73 

4i93 

3o82 

i325 

7.0091 

3o 

45 

2611 

2241 

97i3 

9281 

68i5 

632i 

39i7 

336i 

ioi9 

o4oi 

i5 

45  o 

2426 

2426 

9497 

9497 

6569 

6569 

364o 

364o 

0711 

0711 

45   o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dist.  6. 

Dist.  7. 

Dist.  8. 

Dist.  9. 

Dist.  10. 

Course. 

142 


MERIDIONAL    PARTS. 


LATITUDE. 

Min. 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

Min. 

O 

o.o 

60.0 

120.0 

1  80. 

240.2 

3oo.2j 

36o.7 

421.  1 

48i.6 

542.2 

6o3. 

664. 

?25.3 

O 

I 

I.O 

61.0 

21.  0 

81.1 

41.2 

01.; 

61.7 

22.1 

82.6 

43.3 

04. 

65. 

26.3 

I 

2 

2.O 

62.0 

22.0 

82.1 

42.2 

02.^ 

62.7 

23.1 

83.6 

44.3 

o5. 

66.1 

27.4 

2 

3 

3.o 

63.o 

23.0 

83.i 

43.2 

o3.4 

63.7 

24-1 

84-6 

45.3 

06.  i 

67.1 

28.4 

3 

4 

4.0 

64-0 

24-0 

84.i 

44.2 

04.4 

64-7 

25.1 

85.6 

46.3 

O7.l 

68.2 

29.4 

4 

5 

5.o 

65.o 

25.0 

85.i 

45.2 

o5.4 

65.7 

26.1 

86.6 

47.3 

08.2 

69.2 

3o.5 

5 

6 

6.0 

66.0 

26.0 

86.1 

46.2 

06.; 

66.7 

27.1 

87.6 

48.3 

09.2 

70.2 

3i.5 

6 

7 

7.0 

67.0 

27.0 

87.1 

47.2 

07.4 

67.7 

28.1 

88.6 

49-3 

10.2 

71.1 

32.5 

7 

8 

8.0 

68.0 

28.0 

88.1 

48.2 

08.; 

68.7 

29.I 

89.6 

5o.3 

II.  2 

72.2 

33.5 

8 

9 

9.0 

69.0 

29.0 

89.1 

49.2 

09.4 

69.7 

3o.i 

9°-7 

5i.4 

12.2 

73.3 

34.5 

9 

10 

10.0 

70.0 

i3o.o 

190.1 

25O.2 

3  io.: 

370.7 

43i.i 

491.7 

552.4 

6l3.2 

674.3 

735.6 

10 

ii 

I  I.O 

71.0 

3i.o 

91.1 

5l.2 

1  1.2 

71.7 

32.1 

92.7 

53.4 

14.2 

75.3 

36.6 

ii 

12 

12.0 

72.0 

32.0 

92.1 

52.2 

12.2 

72.7 

33.i 

93.7 

544 

15.3 

76.3 

37.6 

12 

i3 

i3.o 

73.o 

33.o 

93.i 

53.2 

1  3.4 

73.7 

34.2 

94-7 

55.4 

i6.3 

77.3 

38.6 

i3 

14 

14.0 

74-0 

34.o 

94.i 

54.2 

i44 

74.7 

35.2 

95.7 

56.4 

17.3 

78.4 

39.6 

i4 

i5 

i5.o 

75.o 

35.o 

95.i 

55.2 

i5.4 

75.7 

36.2 

96.7 

57.4 

i8.3 

79-4 

4o.7 

i5 

16 

16.0 

76.0 

36.o 

96.i 

56.2 

16.4 

76.8 

3?.2 

97-7 

58.4 

i9.3 

80.4 

4i.7 

16 

J7 

17.0 

77.0 

37.o 

97-i 

57.2 

i7.5 

77.8 

38.2 

98.7 

59.4 

20.3 

81.4 

42.7 

ll 

18 

18.0 

78.0 

38.o 

$8.1 

58.2 

i8.5 

78.8 

39.2 

99.8 

6o.5 

21.3 

82.4 

43.7 

18 

*9 

19.0 

79.0 

39.o 

99.i 

59.2 

i9.5 

79.8 

4o.2 

5oo.8 

6i.5 

22.4 

83.5 

44.8 

'9 

20 

2O.O 

80.0 

i4o.o 

200.  i 

260.2 

320.5 

38o.8 

44i.2 

5oi.8 

562.5 

623.4 

684.5 

745.8 

20 

21 

21.0 

81.0 

4i.o 

OI.I 

61.3 

21.5 

81.8 

42.2 

02.8 

63.5 

24.4 

85.5 

46.8 

21 

22 

22.0 

82.0 

42.0 

02.1 

62.3 

22.5 

82.8 

43.2 

o3.8 

64.5 

25.4 

86.5 

47-8 

22 

23 

23.0 

83.o 

43.o 

o3.i 

63.3 

23.5 

83.8 

44.2 

o4.8 

65.5 

26.4 

87.5 

48.9 

23 

24 

24.0 

84.o 

44-0 

04.  1 

64-3 

24-5 

84-8 

45.2 

o5.8 

66.6 

27.4 

88.6 

49-9 

24 

25 

25.0 

85.o 

45.o 

o5.i 

65.3 

25.5 

85.8 

46.3 

06.8 

67.6 

28.5 

89.6 

5o.9 

25 

26 

26.0 

86.0 

46.o 

06.  i 

66.3 

26.5 

86.8 

47-3 

07.8 

68.6 

29.5 

90.6 

5r.9 

26 

27 

27.0 

87.0 

47.o 

07.1 

67.3 

27.5 

87.8 

48.3 

08.9 

69.6 

3o.5 

91.6 

53.o 

27 

28 

28.0 

88.0 

48.o 

08.  i 

68.3 

28.5 

88.8 

49.3 

09.9 

7o.6 

3i.5 

92.6 

54.0 

28 

29 

29.0 

89.0 

49.0 

o9.i 

69.3 

29.5 

89.8 

5o.3 

10.9 

71.6 

32.5 

93.6 

55.o 

29 

3o 

3o.o 

90.0 

i5o.o 

2IO.I 

270.3 

33o.5 

39o.8 

45i.3 

511.9 

572.6 

633.5 

694.7 

756.o 

3o 

3i 

3i.o 

91.0 

5i.o 

II.  I 

7i.3 

3i.5 

91.8 

52.3 

12.9 

73.7 

34-6 

95.7 

57.i 

3i 

32 

32.0 

92.0 

52.0 

12.  1 

72.3 

32.5 

92.9 

53.3 

i3.9 

74.7 

35.6 

96.7 

58.i 

32 

33 

33.o 

93.0 

53.i 

I3.I 

73.3 

33.5 

93.9 

54.3 

i4.9 

75.7 

36.6 

97-7 

59.i 

33 

34 

34.o 

94.0 

54-1 

14.1 

74.3 

34-5 

94-9 

55.3 

<5.9 

76.7 

37.6 

98.7 

60.  i 

34 

35 

35.o 

95.0 

55.i 

i5.i 

75.3 

35.5 

95.9 

56.3 

i6.9 

77-7 

38.6 

99.8 

61.1 

35 

36 

36.o 

96.0 

56.i 

16.1 

76.3 

36.5 

96.9 

57.3 

18.0 

78.7 

39.6 

700.8 

62.2 

36 

3? 

37.o 

97.0 

57.i 

17.1 

77.3 

37.5 

97-9 

58.4 

I9.o 

79-7 

4o.7 

01.8 

63.2 

37 

38 

38.o 

98.0 

58.i 

18.1 

78.3 

38.5 

98.9 

59.4 

20.  o 

80.8 

4i-7 

02.8 

64.2 

38 

39 

39.0 

99.0 

59.1 

i9.i 

79-3 

39.6 

99-9 

60.4 

21.0 

81.8 

42.7 

o3.8 

65.2 

39 

4o 

4o.o 

IOO.O 

1  60.  i 

220.2 

280.3 

34o.6 

oo.9 

46i.4 

522.0 

82.8 

643.7 

04.9 

66.3 

4o 

4i 

4i.o 

01.  0 

61.1 

21.2 

8i.3 

4i.6 

01.  9 

62.4 

23.0 

83.8 

44.  7 

©5.9 

67.3 

4i 

4s 

42.0 

O2.  0 

62.1 

22.2 

82.3 

42.6 

02.  9 

63.4 

24.O 

84-8 

45.8 

06.9 

68.3 

42 

43 

43.o 

o3.o 

63.i 

23.2 

83.3 

43.6 

o3.9 

64-4 

25.  0 

85.8 

46.8 

07.9 

69.3 

43 

44 

44-0 

o4.o 

64-1 

24.2 

84.3 

44-6 

o4-9 

65.4 

26.0 

86.8 

47.8 

09.0 

70.4 

44 

45 

45.o 

o5.o 

65.i 

25.2 

85.3 

45.6 

o5.9 

66.4 

27.1 

87.9 

48.8 

IO.O 

7i.4 

45 

46 

46.o 

06.0 

66.1 

26.2 

86.3 

46.6 

07.0 

67.4 

28.1 

88.9 

49.8 

I  I.O 

72-4 

46 

4? 

47-0 

07.0 

67.i 

27.2 

87.3 

47.6 

08.0 

68.4 

29.I 

89.9 

5o.8 

12.0 

73.4 

47 

48 

48.o 

08.0 

68.1 

28.2 

88.3 

48.6 

o9.o 

69.5 

3o.i 

9°-9 

5i.9 

i3.i 

74.5 

48 

49 

49.0 

09.0 

69.1 

29.2 

89.3 

49.6 

IO.O 

7o.5 

3i.i 

91.9 

52.  9 

i4.x 

75.5 

49 

5o 

5o.o 

IIO.O 

I7O.I 

230.2 

29o.3 

35o.6 

II.  O 

47i.5 

532.1 

92.9 

653.9 

i5.i 

76.5 

5o 

5i 

5i.o 

II.  0 

71.1 

31.2 

91.3 

5i.6 

12.0 

72.5 

33.i 

93.9 

54-9 

16.1 

77.5 

5i 

52 

52.0 

12.  0 

72.1 

32.2 

92-4 

52.6 

i3.o 

73.5 

34.i 

*  r 

95.o 

55.9 

17.1 

78.6 

52 

53 

53.o 

i3.o 

73.i 

33.2 

93.4 

53.6 

14.0 

74.5 

35.i 

96.o 

57.o 

18.2 

79-6 

53 

54 

54.o 

14.0 

74.1 

34-2 

94.4 

54.6 

i5.o 

75.5 

36.2 

97-° 

58.o 

19.2 

80.6 

54 

55 

55.o 

i5.o 

75.i 

35.2 

95.4 

55.6 

16.0 

76.5 

37.2 

98.o 

59.o 

2O.2 

81.7 

55 

56 

56.o 

16.0 

76.i 

36.2 

96.4 

56.6 

17.0 

77.5 

38.2 

99.o 

60.0 

21.2 

82.7 

56 

5? 

57.o 

17.0 

77.i 

37.2 

97-4 

57.6 

18.0 

78.5 

39.2 

600.0 

61.0 

22.3 

83.7 

5? 

58 

58.o 

18.0 

78.1 

38.2 

98.4 

58.6 

I9.0 

79.5 

4O.2 

OI.O 

62.1 

23.3 

84.7 

58 

59 

59.0 

19.0 

•79.1 

39.2 

99.4 

59.7 

20.0 

8o.5 

41.2. 

02.  1 

63.i 

24.3 

85.8 

59 

MERIDIONAL    PARTS. 


148 


LATITUDE. 

T 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

.s 

0 

786.8 

848.5 

910.5 

972.7 

io35.3 

1098.2 

n6i.5 

1225.  1 

1289.2 

i353.7 

i4i8.6 

i484.i 

o 

i 

87.8 

49-5 

11.  5 

73.8 

36.3 

99.3 

62.5 

26.2 

90.3 

54-8 

19.7 

85.2 

I 

2 

88.8 

5o.5 

12.6 

74-8 

37.4 

i  loo.S 

63.6 

27.3 

91.3 

55.8 

20.8 

86.3 

2 

3 

89.9 

5i.6 

i3.6 

75.9 

38.4 

01.4 

64-7 

28.3 

92.4 

56.9 

21.9 

87.3 

3 

4 

90.9 

52.6 

i4-6 

76.9 

39.5 

02.4 

65.7 

294 

93.5 

58.o 

23.0 

88-4 

4 

5 

91.9 

53.6 

i5.7 

78.0 

4o.5 

o3.5 

66.8 

3o.4 

94.5 

59.0 

24*1 

89.5 

5 

6 

92.9 

54.7 

16.7 

79.0 

4i.6, 

o4.5 

67.8 

3i.5 

95.6 

60.1 

25-1 

qo.6 

6 

7 

94.0 

55.7 

17.7 

80.0 

42.6 

o5.6 

68.9 

32.6 

96.7 

61.2 

26-2 

91.7 

7 

8 

95.0 

56.7 

18.8 

81.1 

43-7 

06.6 

7o.o 

33.6 

97.8 

62.3 

27.3 

92.8 

8 

9 

96.0 

57.8 

19.8 

82.1 

44-7 

07.7 

7i.o 

34-7 

98.8 

63.4 

28.4 

93.9 

9 

10 

797.0 

858.8 

920.8 

983.2 

io45.8 

1108.7 

II72.I 

1235.8 

1299.9 

i364.5 

1429.5 

i495.o 

10 

ii 

98.1 

59.8 

21.9 

84.2 

46.8 

09.8 

73.i 

36.8 

iSoi.o 

65.6 

3o.6 

96.1 

ii 

12 

99.1 

60.9 

22.9 

85.2 

47-9 

10.8 

74-2 

37-9 

O2.O 

66.6 

3i.9 

97-2 

12 

i3 

800.1 

61.9 

23.9 

86.3 

48.9 

11.9 

75.2 

39.0 

o3.i 

67.7 

32.8 

98.3 

i3 

i4 

01.2 

62.9 

25.  0 

87.3 

49.9 

12.9 

76.3 

4o.o 

04.2 

68.8 

33.9 

99.4 

i4 

i5 

O2.  2 

64.o 

26.0 

88.4 

5i.o 

i4-o 

77-4 

4i.i 

o5.3 

69.9 

34-9 

i5oo.5 

i5 

16 

03.2 

65.o 

27.0 

89.4 

52.0 

1  5.o 

78.4 

42.2 

o6.3 

70.9 

36.o 

01.6 

16 

ll 

O4.2 

66.0 

28.1 

90.4 

53.1 

16.1 

79.5 

43.2 

07.4 

72.O 

37.i 

02.7 

*7 

18 

o5.3 

67.1 

29.1 

9i.5 

54.i 

17.1 

8o.5 

44-3 

o8.5 

73.i 

38.2 

o3.8 

18 

'9 

o6.3 

68.1 

3o.i 

92.5 

55.2 

18.2 

81.6 

45.4 

09.6 

74.2 

39.3 

04.9 

'9 

20 

807.3 

869.1 

931.2 

993.6 

io56.2 

1119.2 

1182.7 

1246.4 

i3io.6 

i375.3 

i44o.4 

i5o6.o 

20 

21 

08.4 

70.1 

32.2 

94-6 

57.3 

20.3 

83.7 

47.5 

11.7 

76.4 

4i.5 

07.1 

21 

22 

09.4 

71.2 

33.3 

95.6 

58.3 

21.3 

84-8 

48.6 

12.8 

77-4 

4a.6 

08.2 

22 

23 

10.4 

72.2 

34.3 

96.7 

59.4 

22.4 

85.8 

49-6 

i3.8 

78.5 

43.7 

OQ.3 

23 

24 

ti.4 

73.2 

35.3 

97-7 

60.4 

23.4 

86.9 

50.7 

i4«9 

79.6 

44-81  10.4 

24 

25 

12.5 

74-3 

36.3 

^8.8 

6i.4 

24.5 

88.0 

5i.8 

16.0 

80.7 

45.8 

1  1.5 

25 

26 

i3.5 

75.3 

374 

99.8 

62.5 

25.5 

89.o 

52.8 

17.1 

81.8 

46.9 

12.6 

26 

27 

i4-5 

76.3 

38.4 

1000.8 

63.5 

26.6 

90.1 

53.9 

18.1 

82.8 

48.o 

i3.7 

27 

28 

i5.5 

77-4 

39.5 

01.9 

64.6 

27.6 

91.1 

55.6 

19.2 

83.9 

49.1 

i4.8 

28 

29 

16.6 

78.4 

4o.5 

02.9 

65.6 

28.7 

92.2 

56.o 

20.3 

85.o 

5o.2 

i5.9 

29 

3o 

817.6 

879-4 

94i.6 

ioo4.o 

1066.7 

1129.7 

II93.2 

1257.1 

i32i.4 

i386.i 

i45i.3 

1517.0 

3o 

3i 

18.6 

8o.5 

42.6 

o5.o 

.67-7 

3o.8 

94.3 

58.2 

22.5 

87.2 

62.4 

18.1 

3i 

32 

19.6 

8i.5 

43.6 

06.  i 

68.8 

3i.8 

95.4 

59.2 

23.5 

88.3 

53.5 

19.2 

32 

33 

20.7 

82.5 

44-7 

07.1 

69.8 

32.9 

96.4 

6o.3 

24.6 

89.4 

54.6 

20.3 

33 

34 

21.7 

83.6 

45.7 

08.1 

70.9 

34.o 

97.5 

61.4 

25.7 

90.4 

55.6 

21.4 

34 

35 

22.7 

84.6 

46.7 

09.2 

72.0 

35.1 

98.5 

62.4 

26.7 

9i.5 

56.7 

22.5 

35 

36 

23.8 

85.6 

47.8 

10.2 

73.o 

36.1 

99.6 

63.5 

27.8 

92.6 

57.8 

23.6 

36 

3? 

24.8 

86.7 

48.8 

n.3 

74.i 

37.2 

1200.7 

64-6 

28.9 

93.7 

58.9 

24.7 

37 

38 

25.8 

87.7 

49-9 

12.3 

75.i 

38.2 

01.7 

65.6 

3o.o 

94-8 

60.0 

25.8 

38 

39 

26.9 

88.7 

5o.9 

i3.4 

76.2 

39.3 

02.8 

66.7 

3i.i 

95.8 

61.1 

26.9 

39 

4o 

827.9 

889.8 

951.9 

ioi4«4 

1077.2 

n4o.3 

1203.9 

1267.8 

i332.i 

1396.9 

1462.2 

i528.o 

4o 

4i 

28.9 

90.8 

53.o 

1  5.4 

78.3 

4i-4 

04.9 

68.8 

33.2 

98.0 

63.3 

29.1 

4i 

42 

29.9 

91.8 

54.o 

i6.5 

79.3 

42.4 

06.0 

69.9 

34.3 

99.1 

644 

30.2 

42 

43 

3i.o 

92.9 

55.i 

i7.5 

80.4 

43.5 

07.1 

71.0 

35.3 

I4OO.2 

65.5 

3i.3 

43 

44 

32.0 

93.9 

56.i 

18.6 

81.4 

44-6 

08.1 

72.1 

36.4 

QI.  3 

66.6 

32.4 

44 

45 

33.o 

94.9 

57.i 

19.6 

82.5 

45.6 

09.2 

73.i 

37.5 

02.4 

67.7 

33.5 

45 

46 

34-1 

96.0 

58.2 

20.6 

83.5 

46.7 

IO.2 

74-2 

38.6 

o3.4 

68.8 

34.6 

46 

4? 

35.i 

97.0 

59.2 

21.7 

84.6 

47-7 

n.3 

75.3 

39.7 

o4-5 

69.8 

35.7 

47 

48 

36.i 

98.0 

60.2 

22.7 

85.6 

48.8 

12.4 

76.3 

40.7 

o5.6 

•70.9 

36.8 

48 

49 

37.2 

99.1 

6i.3 

23.8 

86.7 

49-9 

1  3.4 

77-4 

4i.8 

06.7 

72.0 

37.9 

49 

5o 

838.2 

900.1 

962.3 

1024.8 

1087.7 

n5o.9 

i2i4-5 

1278.5 

i34a.9 

1407.8 

i473.i 

iSSg.o 

5o 

5i 

39.2 

01.  1 

63.4 

25.9 

88.8 

52.O 

i5.5 

79.5 

44.o 

08.8 

74.2 

4o.i 

5i 

62 

4O.2 

O2.  2 

644 

26.9 

89.8 

53.o 

16.6 

80.6 

45.i 

09.9 

75.3 

41.2 

52 

53 

4i.3 

03.2 

65.5 

28.0 

9°  9 

54.i 

17.7 

81.7 

46.i 

II.  O 

76.4 

42.3 

53 

54 

42.3 

o4.3 

66.5 

29.0 

91.9 

55.i 

18.7 

82.8 

47.2 

12.  1 

77.5  43-4 

54 

55 

43.3 

o5.3 

67.5 

3o.i 

93.o 

56.2 

19.8 

83.8 

48.3 

13.2 

78.6  44-5 

55 

56 

444 

o6.3 

68.6 

3i.i 

94.0 

57.2 

20.9 

84-9 

49.4 

i4.3 

79-7  45.6 

56 

5? 

45.4 

07.4 

69.6 

,  32.2 

95.i 

58.3 

21.9 

86.0 

5o.4 

1  54 

80.8  46.7 

57 

58 

46.4 

08.4 

70.7 

33.2 

96.1 

59.4 

23.0 

87.0 

5i,5 

i6.5 

81.9  47.8 

58 

59 

47-5 

09.4 

71.7 

34.3 

97.2 

60.4 

24.1 

88.1 

52.6 

i7.5 

83.o  48.9 

59 

MERIDIONAL    PARTS. 


LATITUDE. 

Min. 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

Mia. 

O 

i55o.o 

iBi6.5 

i683.5 

1751.2 

1819.4 

1888.4 

i958.o 

2028.4 

2099.5 

2171.5 

2244.3 

O 

I 

5i.i 

17.6 

84.6 

52.3 

2O.6 

89.5 

59.2 

29.6 

2IOO.7 

72.7 

45.5 

I 

2 

52.2 

18.7 

85.8 

53.4 

21.7 

90.7 

60.4 

30.7 

01.9 

73.9 

46.8 

2 

3 

53.3 

19.8 

86.9 

54.6 

22.9 

91.9 

61.6 

3i.9 

o3.i 

75.i 

48.o 

3 

4 

54-4 

20.9 

88.0 

55.7 

24.0 

93.0 

62.7 

33.i 

o4.3 

76.3 

49.2 

4 

5 

55.5 

22.O 

89.1 

56.8 

25.2 

94.1 

63.9 

34-3 

o5.5 

77.5 

5o.4 

5 

6 

56.6 

23.2 

9o.3 

58.o 

26.3 

95.3 

65-.0 

35.5 

06.7 

78.7 

5i.6 

6 

7 

57-7 

24.3 

91.4 

59.i 

27.5 

96.5 

66.2 

36.7 

07.9 

80.0 

52.  9 

7 

8 

58.8 

25.4 

92.5 

60.2 

28.6 

97-6 

67-4 

37.8 

09.1 

81.2 

54.1 

8 

9 

59.9 

26.5 

93.6 

61.4 

29.7 

98.8 

68.5 

39.o 

io.3 

82.4 

55.3 

9 

10 

i56i.o 

1627.6 

1694.8 

1762.5 

1830.9 

i899.9 

i969.7 

2040.2 

21  II.  5 

2i83.6 

2256.5 

10 

ii 

62.1 

28.7 

95-9 

63.6 

32.0 

I9OI.I 

7°-9 

4i.4 

12.7 

84-8 

57.8 

ii 

12 

63.2 

29.8 

97-° 

64.8 

33.2 

02.3 

72.0 

42.6 

i3.9 

86.0 

59.o 

12 

i3 

644 

3i.o 

98.i 

65.9 

34.3 

o3.4 

73.2 

43.8 

87.2 

60.2 

i3 

i4 

65.5 

32.1 

99.3 

67.0 

35.5 

04.6 

744 

44.9 

i6.3 

88.4 

61.4 

i4 

i5 

66.6 

33.2 

1700.4 

68.2 

36.6 

05.7 

75.6 

46.i 

!7.5 

89.6 

62.7 

i5 

16 

67.7 

34.3 

oi.5 

69.3 

37.8 

06.  9 

76.8 

47.3 

18.7 

9o.8 

63.9 

16 

i7 

68.8 

35.4 

02.  6 

70.5 

38.9 

08.1 

77-9 

48.5 

19.8 

92.0 

65.i 

17 

18 

69.9 

36.5 

o3.8 

71.6 

4o.i 

09.2 

79.1 

49-7 

21.0 

93.3 

66.3 

18 

19 

71.0 

37.6 

o4-9 

72.7 

41.2 

10.4 

80.2 

5o.8 

22.2 

94-4 

67.5 

'9 

20 

1572.1 

i638.8 

1706.0 

1773.9 

1842.4 

i9n.5 

1981.4 

2O52.O 

2123.4 

2i95.7 

2268.8 

20 

21 

73.2 

39.9 

07.1 

75.o 

43.5 

12.7 

82.6 

53.2 

24.6 

96.9 

70.0 

21 

22 

74.3 

4i.o 

o8.3 

76.1 

44.6 

i3.8 

83.7 

54.4 

25.8 

98.1 

71.2 

22 

23 

42.1 

o9.4 

77.2 

45.8 

i5.o 

84-9 

55.6 

27.0 

99.3 

72.5 

23 

24 

76.5 

43.2 

io.5 

78.4 

46.9 

16.2 

86.1 

56.8 

28.2 

2200.5 

73.7 

24 

25 

77.6 

44-3 

n.6 

79.5 

48.i 

I7.3 

87.3 

58.o 

^9.4 

01.7 

74.9 

25 

26 

78.7 

45.5 

12.8 

80.6 

49.2 

i8.5 

88.4 

59.i 

3o.6 

o3.o 

76.1 

26 

27 

79.8 

46.6 

i3.9 

81.8 

5o.4 

i9.6 

89.6 

6o.3 

3i.8 

04.2 

'  77-4 

27 

23 

8o.9 

47-7 

i5.o 

83.o 

5i.5 

20.8 

90.8 

6i.5 

33.o 

o5.4 

78.6 

28 

29 

Bft.i 

48.8 

16.1 

84-1 

52.7 

21.9 

92.0 

62.7 

34.2 

06.6 

79-8 

29 

3o 

i583.2 

i649.9 

1717.3 

1785.2 

1853.8 

1923.1 

I993.i 

2o63.9 

2i35.4 

2207.8 

2281.0 

3o 

3i 

84.3 

5i.o 

18.4 

86.4 

55.o 

24-3 

94.3 

65.1 

36.6 

09.0 

82.3 

3i 

32 

85.4 

52.2 

i9.5 

87.5 

56.i 

25.4 

95.5 

06.2 

37.8 

10.2 

83.5 

32 

33 

86.5 

53.3 

20.7 

88.6 

57.2 

26.6 

96.6 

67-4 

39.o 

11.4 

84-7 

33 

34 

87.6 

54.4 

21.8 

89.8 

58.4 

27.8 

97-8 

68.6 

40.2 

12.7 

86.0 

34 

35 

88.7 

55.5 

22.9 

90.9 

59.6 

28.9 

99.0 

69.8 

4i-4 

13.9 

87.2 

35 

36 

89.8 

56.6 

24.0 

92.1 

60.7 

3o.i 

2OOO.2 

71.0 

42.6 

i5.i 

88.4 

36 

37 

9°-9 

57.8 

25.2 

93.2 

61.9 

3i.3 

01.3 

72.2 

43.8 

i6.3 

89-7 

37 

38 

92.O 

58.9 

26.3 

94.3 

63.o 

32.4 

02.5 

73.4 

45.o 

i7.5 

9°-9 

38 

39 

93.i 

60.0 

27.4 

95.5 

64.2 

33.6 

03.7 

74-5 

46.2 

18.7 

92.1 

39 

4o 

i594.3 

1661.1 

1728.6 

i796.6 

i865.3 

1934.7 

2004.9 

2075.7 

2i47-4 

2219.9 

2293.3 

4o 

4i 

95.4 

62.2 

29.7 

97-8 

66.5 

35.9 

06.0 

76.9 

48.6 

21.2 

94.6 

4i 

42 

96.5 

63.4 

3o.8 

98.9 

67.6 

37.i 

07.2 

78.1 

49.8 

22.4 

95.8 

42 

43 

97-6 

64.5 

31.9 

1800.0 

68.8 

38.2 

08.4 

79-3 

5i.o 

23.6 

97-° 

43 

44 

98.7 

65.6 

33.1 

OI.2 

69.9 

39.4 

09.6 

8o.5 

52.2 

24.8 

98.3 

44 

45 

99.8 

66.7 

34.2 

02.3 

71.1 

4o.5 

10.7 

81.7 

53.4 

26.0 

99.5 

45 

46 

1600.9 

67.8 

35.3 

o3.5 

72.2 

4i.7 

11.9 

82.9 

54.6 

27.2 

2300.7 

46 

47 

02.0 

69.o 

36.5 

o4.6 

73.4 

42.9 

84.o 

55.8 

28.5 

02.  o 

47 

48 

o3.i 

70.1 

37.6 

o5.7 

74.5 

44.o 

14:3 

85.2 

57.0 

29.7 

03.2 

48 

49 

04.2 

71.2 

38.7 

o6.9 

75.7 

45.2 

i5.4 

86.4 

58.2 

3o.9 

o4-4 

49 

5o 

i6o5.4 

i672.3 

I739-9 

1808.0 

1876.8 

1946.4 

2016.6 

2o87.6 

2i59.4 

2232.1 

23o5.7 

5o 

5i 

o6.5 

73.4 

4i.o 

O9.2 

78.0 

47.5 

17.8 

88.8 

60.7 

33.3 

06.  9 

5i 

52 

07.6 

74.5 

42.1 

io.3 

79.2 

48.7 

19.0 

9o.o 

61.9 

34.6 

08.1 

52 

53 

08.7 

75.7 

43.2 

n.4 

8o.3 

49.9 

2O.2 

91.2 

63.i 

35.8 

o9-4 

53 

54 

09.8 

76.8 

444 

12.6 

8i.5 

5i.o 

21.3 

92.4 

64-3 

37.o 

10.6 

54 

55 

10.9 

77-9 

45.5 

i3.7 

82.6 

52.2 

22.5 

93.6 

65.5 

38.2 

u.8 

55 

56 

12.0 

79-° 

46.6 

i4.9 

83.8 

53.4 

23.7 

94-8 

66.7 

39.4 

i3.i 

56 

5? 

i3.i 

80.2 

47.8 

1  6.0 

84-9 

54.5 

24.9 

96.0 

67.  9 

40.7 

i4.3 

57 

58 

14.2 

8i.3 

48.9 

17.2 

86.1 

55.7 

26.0 

97-1 

69  i 

41.9 

i5.5  58 

59 

1  5.4 

82.4 

5o.o 

i8.3 

87.2 

56.9 

27.2 

98.3 

70.3 

43.i   16.8  59 

MERIDIONAL    PARTS. 


LATITUDE. 

Min. 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

Mill. 

0 

23i8.o 

2392.6 

2468.3 

2545.o 

2622.7 

2701.6 

2781.7 

2863.1 

2945.8 

3o3o.o 

3n5.6 

0 

I 

19.2 

93-9 

69.5 

46.2 

24.0 

02.9 

83.i 

64.5 

47.2 

3i4 

I7.0 

I 

2 

20.  5 

95.i 

70.8 

47.5 

25.3 

o4-3 

844 

65.8 

48.6 

32.8 

i8.5 

2 

3 

21.7 

96.4 

72.1 

48.8 

26.6 

o5.6 

85.8 

67.2 

5o.o 

34.2 

19.9 

3 

4 

23.0 

97-7 

734 

5o.i 

27.9 

06.9 

87.1 

68.5 

5i4 

35.6 

21.4 

4 

5 

24.2 

98.9 

74-6 

5i.4 

29.2 

o8.3 

88.5 

7o.o 

52.8 

37.0 

22.8 

5 

6 

25.4 

2400.2 

75.9 

52.  7 

3o.5 

09.6 

89.8 

71.3 

54-2 

384 

24.2 

6 

7 

26.7 

01.4 

77.1 

54.o 

31.9 

10.9 

91.2 

72-7 

55.6 

39.8 

25.  7 

7 

8 

27.9 

02.7 

78.5 

55.3 

33.2 

12.2 

92.5 

74.i 

57.0 

4i.3 

27.1 

8 

9 

29.1 

03.9 

79-7 

56.6 

34-5 

i3.5 

93.8 

754 

58.3 

42.7 

28.5 

9 

10 

233o.4 

24o5.2 

2481.0 

2557.8 

2635.8 

2714.9 

2795.i 

2876.8 

2959.8 

3o44-i 

3i3o.o 

10 

ii 

3i.6 

06.4 

82.2 

59.i 

37.i 

16.2 

96.5 

78.2 

61.1 

45.5 

3i.5 

ii 

12 

32.9 

07.7 

83.5 

60.4 

38.4 

17.5 

97-9 

79.5 

62.5 

47.0 

32.9 

12 

i3 

34.i 

09.0 

84.8 

61.7 

39-7 

18.9 

99-3 

8o.9 

63.9 

484 

34.3 

i3 

i4 

35.3 

1O.2 

86.1 

63.o 

4i.o 

20.  2 

2800.6 

82.3 

65.3 

49.8 

35.8 

i4 

i5 

36.6 

ii.  5 

87.4 

64.3 

42.3 

21.5 

02.0 

83.  7 

66.7 

5l.2 

37.2 

i5 

16 

37.8 

12.7 

88.6 

65.6 

43.6 

22.9 

o3.3 

85.o 

68.1 

52.6 

38.7 

16 

I7 

39.0 

14.0 

89.9 

66.9 

44.9 

24.2 

o4-7 

864 

69.5 

54-1 

4o.i 

17 

18 

4o.3 

15.2 

91.2 

68.2 

46.3 

25.5 

06.0 

87.8 

7°-9 

55.5 

4i.6 

18 

J9 

4i.5 

i6.5 

92.4 

69.5 

47.6 

26.8 

o7.3 

89.1 

72.3 

56.9 

43.o 

19 

20 

2342.8 

2417-8 

2493.7 

2570.7 

2648.9 

2728.2 

2808.8 

2890.5 

2973.7 

3o58.3 

3i44-5 

20 

21 

44.o 

19.0 

95.0 

72.0 

5o.a 

29.5 

IO.I 

91.9 

76.1 

59.7 

45.9 

21 

22 

45.3 

20.3 

96.3 

73.3 

5i.5 

3o.8 

n4 

93.3 

76.5 

61.2 

474 

22 

23 

46.5 

21.5 

97.6 

74-6 

52.8 

32.2 

12.8 

94.7 

77-9 

62.6 

48.8 

23 

24 

47-7 

22.8 

98.8 

75.9 

54-1 

33.5 

14.1 

96.0 

79-3 

64-o 

5o.3 

24 

25 

49.0 

24.O 

2500.1 

77.2 

55.5 

34-8 

i5.5 

974 

80.7 

654 

5i.7 

25 

26 

5o.2 

25.3 

01.4 

78.5. 

56.8 

36.2 

16.8 

98.8 

82.1 

66.9 

53.2 

26 

27 

5i.5 

26.5 

02.7 

79.8 

58.i 

37.5 

18.2 

2900.2 

83.5 

68.3 

54.6 

27 

28 

52.7 

27.8 

03.9 

81.1 

59.4 

38.8 

i9.5 

0!.5 

84-9 

69.7 

56.i 

28 

29 

54.o 

29.1 

05.2 

82.4 

60.  7 

4O.2 

20.  9 

02.9 

86.3 

71.1 

57.5 

29 

3o 

2355.2 

243o.3 

25o6.5 

2583.7 

2662.0 

274l.5 

2822.3 

2904.3 

2987.7 

3072.6 

SiSg.o 

3o 

3i 

56.5 

3i.6 

07.8 

86.0 

63.3 

42.9 

23.6 

o5.7 

89.1 

74-0 

60.4 

3i 

32 

57.7 

32.9 

09.0 

86.3 

64-6 

44-2 

25.0 

o7.i 

90.5 

754 

61.9 

32 

33 

58.9 

34.i 

io.3 

87.6 

66.0 

45.5 

26.3 

08.4 

91.9 

76.9 

63.3 

33 

34 

60.2 

35.4 

ii.  6 

88.9 

67.3 

46.9 

27.7 

°9-7 

93.3 

78.3 

G4.8 

34 

35 

61.4 

36.7 

12.9 

90.2 

68.6 

48.2 

29.0 

II.  2 

94.7 

79-7 

66.2 

35 

36 

62.7 

37.9 

14.2 

9i.5 

69.9 

49-5 

3o4 

12.6 

96.1 

81.1 

67.7 

36 

3? 

63.9 

39.2 

1  5.4 

92.8 

71.2 

50.9 

3i.7 

i4«o 

97.5 

82.6 

69.1 

37 

38 

65.2 

4o.4 

16.7 

94.1 

72.5 

52.2 

33.i 

i5.3 

98.9 

84.o 

70.6 

38 

39 

66.4 

4i-7 

18.0 

95.4 

73.9 

53.5 

34.5 

16.7 

3ooo.3 

854 

72.0 

39 

4o 

2367.6 

2443.0 

2519.3 

2596.7 

2675.2 

2754.9 

2835.8 

2918.1 

3ooi.8 

3o86.9 

3i73.5 

4o 

4i 

68.9 

44.2 

20.  5 

98.0 

76.5 

56.2 

37.2 

i9.5 

03.2 

88.3 

75.o 

4i 

42 

70.2 

45.5 

21.8 

99.3 

77.8 

57.6 

38.6 

20.9 

04.6 

89.7 

76.4 

42 

43 

71.4 

46.8 

23.1 

2600.5 

•79.1 

58.9 

39.9 

22.3 

06.0 

91.2 

77-9 

43 

44 

72.6 

48.o 

244 

01.9 

8o.5 

60.2 

4i-3 

23.6 

o74 

92.6 

79.3 

44 

45 

73.9 

49.3 

25.7 

03.2 

81.8 

6i.5 

42.6 

25.0 

08.8 

94-o 

80.8 

45 

46 

75.i 

5o.6 

27.0 

o4.5 

83.i 

62.9 

44.o 

26.4 

IO.2 

95.5 

82.3 

46 

4? 

76.4 

5i.8 

28.3 

o5.8 

844 

64-3 

454 

27.8 

ii.  6 

96.9 

83.7 

47 

48 

77.6 

53.i 

29.5 

07.1 

85.7 

65.6 

46.7 

29.2 

i3.o 

98.3 

85.2 

48 

49 

78.9 

54-3 

3o.8 

08.4 

87.1 

66.9 

48.i 

3o.6 

i44 

99-7 

86.6 

49 

5o 

238o.i 

2455.6 

2532.1 

2609.7 

2688.4 

2768.3 

2849.5 

2932.0 

3oi5.8 

SlOI.2 

3i88.i 

5o 

5i 

81.4 

56.9 

33.4 

II.  O 

89.7 

69.6 

5o.8 

33.3 

I7.2 

02.  6 

89.6 

5i 

52 

82.6 

58.i 

34.7 

12.3 

91.0 

71.0 

52.2 

34-7 

18.7 

o4.i 

91.0 

52 

53 

83.9 

59.4 

36.o 

i3.6 

92.3 

72.3 

53.5 

36.i 

20.1 

o5.6 

92.5 

53 

54 

85.i 

60.7 

37.2 

i4.9 

93.7 

73.7 

54-9 

37.5 

21.5 

O7.O 

94.0 

54 

55 

86.4 

61.9 

38.5 

16.2 

95.o 

75.0 

56.3 

38.9 

22-9 

08.4 

95.4 

55 

56 

87.6 

63.2 

39.8 

17.5 

96.3 

76.3 

57.7 

4o.3 

24-3 

o9.8      96.9    56 

57 

88.9 

64.5 

4i.i 

18.8 

97.6 

77-7 

59.o 

4i,7 

25.  7 

ii.  2      98.4    57 

58 

90.2 

65.8 

42-4 

2O.I 

99.0 

79-° 

6o.5 

43.i 

27.1 

12.7      998    58 

59 

91.4 

67.0 

43.6 

21-4 

2700.3 

80.4 

61.1 

444 

28.5 

14.1^3201.3:   59 

146 


MERIDIONAL    PARTS. 


LATITUDE. 

Min. 

47° 

48° 

49° 

50° 

51° 

52° 

53° 

54° 

55° 

56° 

57° 

Min. 

o 

3202.7 

3291.5 

3382.1 

3474.5 

3568.8 

3665.2 

3763.8 

3864.6 

3968.o 

4o73-9 

4182.6 

o 

I 

O4«2 

93.0 

83.6 

76.0 

•70.4 

66.8 

65.4 

66.3 

69.7 

75.7 

84.5 

I 

2 

05.7 

94.5 

85.i 

77.6 

72.O 

08.4 

67.1 

68.0 

7i.5 

77.5 

86.3 

2 

3 

07.1 

96.0 

86.7 

79.i 

73.6 

7O.I 

68.8 

69-7 

73.2 

79.3 

88.1 

3 

4 

08.6 

97.5 

88.2 

80.7 

75.2 

71.7 

7o.4 

7i.5 

75.0 

81.1 

90.0 

4 

5 

I  O.I 

99.0 

89.7 

82.3 

76.8 

73.3 

72.1 

73.2 

76.7 

82.9 

91.8 

5 

6 

n.5 

33oo.5 

9i.3 

83.8 

78.4 

75.o 

73.7 

74.9 

78.4 

84.7 

93.7 

6 

7 

i3.o 

O2.O 

92.8 

85.4 

79-9 

76.6 

75.4 

76.6 

80.2 

86.4 

95.5 

7 

8 

i4-5 

o3.5 

94.3 

87.0 

8i.5 

•78.2 

77.1 

78.3 

82.0 

88.2 

97.3 

8 

9 

i5.9 

o5.o 

95.8 

88.5 

83.i 

79.8 

78.7 

80.0 

83.7 

9o.o 

99.2 

9 

10 

3217.4 

33o6.5 

3397.4 

349o.i 

3584.7 

368i.5 

3780.4 

388i.7 

3985.4 

4091.8 

4201.0 

10 

ii 

18.9 

08.0 

98.9 

91.6 

86.3 

83.i 

82.1 

83.4 

87.2 

93.6 

02.9 

ii 

12 

20.3 

09.5 

34oo.4 

93.2 

87.9 

84.7 

83.7 

85.i 

88.9 

95.4 

o4«7 

12 

i3 

21.8 

II.  O 

02.  o 

94.7 

89.5 

86.4 

85.4 

86.8 

9°-7 

97.2 

06.6 

i3 

i4 

23.3 

12.5 

o3.5 

96.3 

91.1 

88.0 

87.1 

88.5 

92.5 

99.0 

08.4 

i4 

l5 

24.8 

i4-o 

o5.o 

97-9 

92.7 

89.6 

88.8 

90.2 

94.2 

4ioo.8 

io.3 

i5 

16 

26.2 

i5.5 

06.6 

99.4 

94.3 

9i.3 

90.4 

92.O 

96.o 

02.6 

12.  1 

16 

!? 

27.7 

17.0 

08.1 

35oi.o 

95.9 

92.9 

92.1 

93.7 

97-7 

04.4 

14.0 

17 

18 

29.2 

i8.5 

o9.6 

02.6 

97.5 

94-5 

93.8 

95.4 

99.5 

06.2 

i5.8 

18 

*9 

30.7 

2O.O 

n.  i 

04.1 

99.i 

96.2 

95.5 

97.I 

4OOI.2 

08.0 

17.7 

19 

2O 

3232.1 

3321.5 

3412.7 

35o5.7 

36oo.7 

3697.8 

3797-1 

3898.8 

4oo3.o 

4109.8 

4219.5 

20 

21 

33.6 

23.0 

14.2 

07.3 

02.3 

99.4 

98.8 

39oo.5 

o4-7 

n.6 

21.4 

21 

22 

35.i 

24-5 

i5.7 

08.8 

o3.9 

37oi.i 

38oo.5 

O2.  2 

o6.5 

i3.4 

23.2 

22 

23 

36.6 

26.0 

i7.3 

10.4 

o5.5 

02.  7 

O2.  2 

04.0 

o8.3 

15.2 

25.1 

23 

24 

38.o 

27.5 

18.8 

12.  0 

O7.I 

o4-4 

o3.8 

©5.7 

IO.O 

17.1 

27.0 

24 

25 

39.5 

29.0 

20.4 

i3.5 

o8.7 

06.0 

o5.5 

07.4 

n.8 

18.9 

28.8 

25 

26 

4i.o 

3o.6 

21.9 

i5.i 

io.3 

o7.6 

07.2 

o9.i 

i3.5 

20.7 

3o.6 

26 

27 

42.5 

32.1 

23.5 

16.7 

n.9 

09.3 

08.9 

10.8 

i5.3 

22.5 

32.5 

27 

28 

44-0 

33.6 

25.  0 

i8.3 

i3.6 

10.9 

io.5 

12.5 

17.1 

24.3 

34.4 

28 

29 

45.4 

35.i 

26.5 

19.8 

i5.i 

12.6 

12.2 

i4.3 

18.8 

26.1 

36.2 

29 

3o 

3246.9 

3336.6 

3428.0 

3521.4 

36i6.7 

37i4.2 

38i3.9 

39i6.o 

4020.6 

4127.9 

4238.1 

3o 

3i 

48.4 

38.1 

29.6 

23.0 

18.4 

i5.8 

i5.6 

17.7 

22.4 

29-7 

4o.o 

3i 

32 

49.9 

39.6 

3i.i 

24.6 

20.0 

i7.5 

i7.3 

i9-4 

24.1 

3i.5 

4i.8 

32 

33 

5i.4 

4i.i 

32.7 

26.1 

21.6 

19.1 

18.9 

21.2 

25.9 

33.3 

43.7 

33 

34 

52.8 

42.6 

34-2 

27.7 

23.2 

20.8 

20.6 

22.  9 

27.7 

35.2 

45.5 

34 

35 

54.3 

44-1 

35.8 

29.3 

24.8 

22.4 

22.3 

24-6 

29.4 

37.o 

47-4 

35 

36 

55.8 

45.7 

37.3 

3o.8 

26.4 

24.1 

24.O 

26.3 

3l.2 

38.8 

49.3 

36 

37 

57.3 

47.2 

,  38.8 

32.4 

28.0 

25.7 

25-7 

28.1 

33.o 

4o.6 

5i.i 

3? 

38 

58.8 

48.7 

4o.4 

34.o 

29.6 

27.4 

274 

29.8 

34-8 

42.4 

53.o 

38 

39 

6o.3 

50.2 

4i.9 

35.6 

3i.3 

29.0 

29.1 

3i.5 

36.5 

44-2 

54-9 

39 

4o 

3261.7 

335i.7 

3443.5 

3537.1 

3632.8 

373o.7 

383o.8 

3933.2 

4o38.3 

4i46.i 

4256.7 

4o 

4i 

63.2 

53.2 

45.o 

38.7 

344 

32.3 

32.4 

35.0 

4o.i 

47«9 

58.6 

4i 

42 

64-7 

54.7 

46.6 

4o.3 

36.i 

34.0 

34.i 

36.7 

4i.8 

49.7 

6o.5 

42 

43 

66.2 

56.2 

48.i 

4  1.  Q 

37.7 

35.6 

35.8 

38.4 

43.6 

5i.5 

62.3 

43 

44 

67.7 

57.8 

49.7 

43.5 

39.3 

37.3 

*37.5 

4o.2 

45.4 

53.4 

64.2 

44 

45 

69.2 

59.3 

5l.2 

45.o 

4o.9 

38.9 

39.2 

41.9 

47-2 

55.2 

66.1 

45 

46 

70.7 

60.8 

52.8 

46.6 

42.5 

4o.6 

40.9 

43.6 

4g.o 

57.o 

68.0 

46 

47 

72.1 

62.3 

54.3 

48.2 

44.i 

42.2 

42.6 

45.4 

5o.7 

58.8 

69.8 

47 

48 

73.6 

63.8 

55.8 

49-8 

45.8 

43.9 

44.3 

47.1 

52.5 

60.7 

71.7 

48 

49 

75.i 

65.4 

57.4 

5i.4 

474 

45.5 

46.o 

48.8 

54.3 

62.5 

73.6 

49 

5o 

3276.6 

3366.9 

3458.9 

3553.0 

3649.o 

3747.2 

3847-7 

395o.6 

4o56.i 

4i64.3 

4275.5 

5o 

5i 

78.! 

68.4 

6o.5 

54.6 

5o.6 

48.8 

49.4 

52.3 

57.8 

66.1 

77-4 

5i 

52 

79.6 

69-9 

62.0 

56.i 

52.2 

5o.5 

5i.i 

54-0 

59.6 

68.0 

79.2 

52 

53 

81.1 

71.4 

63.6 

57.7 

53.8 

52.1 

52.8 

55.8 

61.4 

69.8 

81.1 

53 

54 

82.6 

73.o 

65.2 

59.3 

55,5 

53.8 

54-4 

57.5 

63.2 

71.6 

83.o 

54 

55 

84.i 

74-5 

66.7 

6o.9 

57.i 

55.5 

56.i 

59.3 

65.o 

73.5 

84.9 

55 

56 

85.6 

76.0 

68.3 

62.5 

58.7 

57.1 

57.8 

61.0 

66.8 

75.3 

86.8 

56 

57 

87.! 

77.5 

69.8 

64-0 

6o.3 

58.8 

59.5 

62.7 

68.5 

77.1 

88.6 

57 

58 

88.5 

79-° 

71-4 

65.6 

61.9 

60.4 

6L2 

64-5 

7o.3 

70.  o 

90.5 

58 

59 

90.0 

80.6 

73.o 

67.2 

63.6 

62.1 

62.  9 

66.2 

72.1 

80.8 

92.4 

59 

MERILIONAL    PARTS. 


LATITUDE. 

Min. 

58° 

59° 

60° 

61° 

62° 

63° 

64° 

65° 

66° 

67° 

68° 

Min. 

o 

4294.3 

4409.1 

4527.4 

4649-2 

4775.0 

49o4-9 

5039.4 

5178.8 

5323.5 

5474.0 

563o.8 

0 

I 

96.2 

n.  i 

29.4 

5i.3 

77.1 

07.1 

4i.7 

81.2 

26.0 

76.6 

33.5 

I 

2 

98.1 

i3.o 

3i.4 

53.4 

79.3 

o9.4 

44.o 

83.5 

28.4 

79.1 

36.2 

2 

3 

[3oo.o 

i5.o 

33.4 

55.4 

81.4 

n.6 

46.3 

85.9 

30.9 

8i.7 

38.8 

3 

4 

01.9 

16.9 

35.4 

57.5 

83.5 

i3.8 

48.6 

88.3 

33.4 

84.3 

4i.5 

4 

5 

03.7 

18.9 

37-4 

59.6 

85.6 

16.0 

5o.9 

9°-7 

35.8 

86.9 

44-2 

5 

6 

o5.6 

20.8 

39.4 

61.6 

87.8 

18.2 

53.i 

93.i 

38.3 

89.4 

46.9 

6 

7 

oy.S 

22.8 

4i-4 

63.7 

89.9 

20.4 

55.4 

•  95.4 

4o.8 

92.0 

49.6 

7 

8 

09.4 

24.7 

43.4 

65.8 

92.1 

22.6 

57.7 

97.8 

43.2 

94-5 

52.3 

8 

9 

n.  3 

26.7 

45.4 

67.8 

94.2 

24.8 

60.0 

52OO.2 

45-7 

97.1 

54.9 

9 

10 

43i3.2 

4428.6 

4547-4 

4669.9 

4796.3 

4927.0 

5o62.3 

52O2.6 

5348.2 

5499.7 

5657.6 

10 

ii 

i5.i 

3o.6 

49.4 

72.0 

98.5 

29.2 

64-6 

o4-9 

5o.7 

55o2.3 

6o.3 

ii 

12 

17.0 

32.5 

5i.4 

74.1 

48oo.6 

3i.5 

66.9 

o7.3 

53.i 

04.9 

63.o 

12 

i3 

18.9 

34.5 

53.5 

76.1 

02.8 

33.7 

69.2 

09-7 

55.6 

07.4 

65.7 

i3 

i4 

20,8 

36.4 

55.5 

78.2 

o4-9 

35.9 

7i.5 

12.  1 

58.i 

IO.O 

68.4 

i4 

i5 

22.7 

38.4 

57.5 

8o.3 

07.1 

38.i 

73.8 

i4.5 

60.6 

12.6 

71.1 

i5 

16 

24.6 

4o.3 

59.5 

82.4 

09,2 

4o.3 

76.1 

i6.9 

63.i 

15.2 

73.8 

16 

J7 

26.5 

42.3 

6i.5 

84-5 

11.4 

42.6 

784 

i9.3 

65.6 

17.8 

76.5 

J7 

18 

28.4 

44-2 

63.5 

86.5 

i3.5 

44.8 

80.7 

21.6 

68.0 

20.4 

79.2 

18 

:9 

3o.3 

46.2 

65.6 

88.6 

i5.7 

47.0 

83.o 

24.0 

70.5 

23.0 

81.9 

J9 

20 

4332.2 

4448.2 

4567.6 

4690.7 

4817.8 

4949.2 

5o85.3 

5226.4 

5373.0 

5525.6 

5684.6 

20 

21 

34.1 

5o.i 

69.6 

92.8 

2O.O 

$i.5 

87.6 

28.8 

75.5 

28.1 

87.3 

21 

22 

36.o 

52.1 

71.6 

94.9 

22.1 

53.7 

9o.o 

3l.2 

78.0 

30.7 

90.0 

22 

23 

37.9 

54.i 

73.6 

97.0 

24-3 

55.9 

92.3 

33.6 

8o.5 

33.3 

92.7 

23 

24 

39.8 

56.o 

75.7 

99.1 

26.4 

58.2 

94.6 

36.o 

83.o 

35-9 

95.5 

24 

25 

4i.8 

58.o 

77-7 

4701.1 

28.6 

6o.4 

96-9 

38.4 

85.5 

38.6 

98.2 

25 

26 

43.7 

60.0 

79-7 

03.2 

3o.8 

62.6 

99-2 

4o.8 

88.0 

41.2 

5700.9 

26 

27 

45.6 

61.9 

81.7 

o5.3 

32.9 

64.9 

5ioi.5 

43.2 

90.5 

43.8 

o3.6 

27 

28 

47-5 

63.9 

83.8 

07.4 

35.i 

67.1 

o3.8 

45.7 

93.0 

46-4 

o6.3 

28 

29 

49.4 

65.9 

85.8 

o9.5 

37.3 

69.4 

06.2 

48.i 

95.5 

49.0 

09.1 

29 

3o 

435i.3 

4467.8 

4587.8 

4711.6 

4839.4 

4971-6 

5io8.5 

525o.5 

5398.0 

555i.6 

57n.8 

3o 

3i 

53.2 

69.8 

89.9 

i3.7 

4i.6 

73.8 

10.8 

52.  9 

54oo.5 

54.2 

i4-5 

3i 

32 

55.i 

71.8 

91.9 

i5.8 

43.8 

76.1 

i3.i 

55.3 

o3.o 

56.8 

i7.3 

32 

33 

57.i 

73.7 

93.9 

17.9 

45.9 

78.3 

i5.5 

57.7 

o5.5 

594 

20.0 

33 

34 

Sg.o 

75.7 

96.0 

2O.O 

48.i 

80.6 

17.8 

60.  i 

08.  i 

62.1 

22.7 

34 

35 

60.9 

77-7 

98.0 

22.1 

5o.3 

82.8 

20.1 

62.6 

10.6 

64-7 

25.5 

35 

36 

62.8 

79-7 

46oo.o 

24-2 

52.4 

85.i 

22.4 

65.o 

i3.i 

67.3 

28.2 

36 

37 

64,7 

81.6 

02.  i 

26.3 

54.6 

87.3 

24.8 

67.4 

i5.6 

69.9 

30.9 

37 

38 

66.7 

83.6 

o4«i 

28,4 

56.8 

89.6 

27.1 

69.8 

18.1 

72.6 

33.7 

38 

39 

68.6 

85.6 

06.1 

3o.5 

59.o 

91.8 

294 

72.2 

2O.6 

76.2 

364 

39 

4o 

437o.5 

4487-6 

4608.2 

4732.6 

486i.i 

4994.1 

5i3i.8 

6274.7 

5423.2 

5577.8 

5739.2 

4o 

4i 

72.4 

89.6 

10.2 

34-7 

63.3 

•    96.3 

34.i 

77.1 

25.7 

80.4 

41.9 

4i 

42 

74-3 

9i.5 

12.3 

36.8 

65.5 

98.6 

36.5 

79.5 

28.2 

83.i 

44-7 

42 

43 

76.3 

93.5 

i4.3 

39.o 

67.7 

5ooo.8 

38.8 

82.0 

3o.8 

85.7 

47.5 

43 

44 

78.2 

95.5 

16.4 

4i.i 

69.9 

o3.i 

4i.i 

844 

33.3 

88.4 

5o.2 

44 

45 

80.  i 

97.5 

18.4 

43.2 

72.0 

o5.4 

43.5 

86.8 

35.8 

91.0 

52.9 

45 

46 

82.1 

99.5 

20.5 

45.3 

74.2 

07.6 

45.8 

89.3 

38.4 

93.6 

55.7 

46 

47 

84.o 

45oi.5 

22.5 

474 

76.4 

09.9 

48.2 

91.7 

40.9 

96.3 

58.5 

47 

48 

85.9 

o3.4 

24.6 

49.5 

78.6 

12.2 

5o.5 

94.1 

434 

98.9 

61.2 

48 

49 

87.8 

o5.4 

26.6 

5i.6 

80.8 

l44 

52.9 

96.6 

46.o 

56oi.6 

64.0 

49 

5o 

4389.8 

4507.; 

4628.7 

4753.7 

4883.0 

5oi6.7 

5i55.2 

5200.0 

5448.5 

56o4-2 

5766.8 

5o 

5i 

91.7 

09.4 

30.7 

55.9 

85.2 

18.9 

57.6 

53oi.5 

5i.o 

06.9 

69.5 

5i 

52 

93.6 

II.  L 

32.8 

58.o 

87.4 

21.2 

59.9 

03.9 

53.6 

o9.5 

72.3 

52 

53 

95.6 

i3.4 

34.8 

60.  i 

89.5 

23.5 

62.3 

o6.3 

56.i 

12.2 

75.i 

53 

54 

97.5 

i5.; 

36.9 

62.2 

91.7 

25.8 

64.6 

08.8 

58.7 

i4.8 

77-9 

54 

55 

99.4 

17.2 

39.o 

64.4 

93.9 

28.0 

67.0 

II.  2 

61.2 

i7.5 

80.6 

55 

56 

44oi.2 

19.4 

4i.o 

66.5 

96.1 

3o.3 

69.4 

i3.7 

63.8 

20.2 

834 

56 

57 

o3.3 

2.1.1. 

43.o 

68.6 

98.3 

32.6 

71.7 

16.1 

66.3 

22.9 

86.2 

57 

58 

o5.3 

23.4 

45.i 

70.7 

49oo.5 

34-9 

74.i 

18.6 

68.9 

25.5 

89.0 

58 

59 

07.2 

25.4 

47.2 

72.9 

02.7 

37.i 

76.4 

21.  1 

7i.4 

28.2 

9i.8 

59 

148 


MERIDIONAL    PARTS. 


LATITUDE. 

Min. 

69° 

70° 

71° 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

79° 

Min. 

O 

5794-6 

5965.9 

6145.7 

6334.8 

65344 

674i).7 

697o.3 

7210.1 

7467.2 

7744-6 

8o45.  7 

O 

I 

97-4 

68.8 

48.8 

38.i 

37.8 

49.4 

74.2 

14.2 

71.7 

49.4 

5i.o 

I 

2 

58oo.i 

71.8 

5i.9 

4i.3 

4i.3 

53.o 

78.1 

i8.3 

76.1 

54-2 

56.2 

2 

3 

02.9 

74-7 

54-9 

44-6 

44-7 

56.6 

81.9 

22.5 

80.6 

59.o 

6i.5 

3 

4 

o5.y 

77.6 

58.o 

47-8 

48.i 

6o.3 

85.8 

26.6 

85.o 

63.9 

66.7 

4 

5 

o8.5 

80.6 

61.1 

5i.i 

5i.6 

63.9 

89.7 

3o.8 

89.5 

68.7 

72.0 

5 

6 

li,3 

83.5 

64-2 

54.3 

55.o 

67.6 

93.6 

35.o 

94.0 

73.5 

.  77-3 

6 

7 

l4«2 

86.4 

67.3 

57.6 

58.5 

71.2 

97.5 

39.i 

98.5 

78.4 

82.6 

7 

8 

17.0 

89.4 

70.4 

60.8 

61.9 

74-9 

7001.4 

43.3 

75o3.o 

83.3 

87.9 

8 

9 

19.8 

92.3 

73.5 

64.i 

65.3 

78.5 

o5.3 

47-5 

07.4 

88.1 

93.2 

9 

10 

5822.6 

SggS.S 

6176.6 

6367.4 

6568.8 

6782.2 

7009.2 

725l.7 

75n.9 

7793.o 

8098.5 

10 

n 

25.4 

98.2 

79-7 

70.6 

72.3 

85.9 

i3.i 

55.8 

i6.5 

97-9 

8io3.8 

ii 

12 

28.2 

6001.2 

82.8 

73.9 

75.7 

89.6 

17.0 

60.0 

21.0 

7802.8 

09.2 

12 

i3 

3i.o 

o4-i 

85.9 

77.2 

79.2 

93.2 

20.9 

64.2 

25.5 

07-7 

14.5 

i3 

i4 

33.8 

07.1 

89.0 

80.4 

82.6 

96.9 

24.8 

68.4 

3o.o 

12.6 

19.9 

i4 

i5 

36.7 

IO.O 

92.1 

83.7 

86.1 

6800.6 

28.8 

72.6 

34-5 

I7.5 

25.2 

i5 

16 

39.5 

1  3.o 

95.2 

87.0 

89.6 

o4.3 

32.7 

76.8 

Sg.i 

22.4 

3o.6 

16 

I7 

42.3 

1  6.0 

98.3 

90.3 

93.0 

08.0 

36.6 

81.1 

43.6 

27.3 

36.o 

J7 

18 

45.i 

18.9 

6201.4 

93.6 

96.5 

n.6 

4o.6 

85.3 

48.i 

32.2 

4i.3 

18 

J9 

48.o 

21.9 

o4.5 

96.9 

6600.0 

1  5.4 

44-5 

89.5 

52.7 

37.2 

46.7 

'9 

20 

585o.8 

6024.9 

6207.7 

64oo.s 

66o3.5 

6819.1 

7048.5 

7293.7 

7557.3 

7842.1 

8i52.i 

20 

21 

53.6 

27.8 

10.8 

o3.4 

07.0 

22.8 

52.4 

98.0 

61.8 

47.i 

57.5 

21 

22 

56.5 

3o.8 

i3.9 

06.7 

!0.5 

26.5 

56.4 

7302.2 

66.4 

52.  0 

62.9 

22 

23 

59.3 

33.8 

17.0 

IO.I 

i4-o 

30.2 

6o.3 

06.4 

71.0 

57.o 

68.4 

23 

24 

62.2 

36.8 

20.2 

i3.4 

17.5 

33.9 

64.3 

10.7 

75.5 

61.9 

73.8 

24 

25 

65.o 

39.8 

23.3 

16.7 

21.0 

37.6 

68.3 

i5.o 

80.  i 

66.9 

79.2 

25 

26 

67.8 

42.7 

26.5 

20.  o 

24.5 

4i.3 

72.2 

19.2 

84-7 

7i.9 

84.7 

26 

87 

70.7 

45.7 

29.6 

23.3 

28.0 

45.i 

76.2 

23.5 

89.3 

76.9 

90.1 

27 

28 

73.5 

48.7 

32.7 

26.6 

3i.5 

48.8 

80.2 

27.7 

93.9 

81.9 

95.6 

28 

29 

76.4 

5i.7 

35.9 

29.9 

35.o 

52.5 

84.2 

32.0 

98.5 

86.9 

8201.1 

29 

3o 

5879.2 

6o54-7 

6239.0 

6433.3 

6638.5 

6856.3 

7088.2 

7336.3 

7603.2 

789I-9 

8206.6 

3o 

3i 

82.1 

57.7 

42.2 

36.6 

42.1 

60.0 

92.2 

4o.6 

07.8 

96.9 

12.  1 

3i 

32 

85.o 

60.7 

45.3 

39.9 

45.6 

63.8 

96.2 

44-9 

12.4 

•7902.0 

I7.6 

32 

33 

87.8 

63.7 

48.5 

43.2 

49'  i 

67.5 

7100.2 

49-2 

17.0 

O7.O 

23.1 

33 

34 

90.7 

66.7 

5i.7 

46.6 

52.6 

7i.3 

O4.2 

53.5 

21.7 

12.0 

28.6 

34 

35 

93.6 

69.7 

54.8 

4y-9 

56.2 

75.0 

08.2 

57.8 

26.3 

I7.I 

34.i 

35 

36 

96.4 

72.7 

58.o 

53.3 

59.7 

78.8 

12.2 

62.1 

3i.o 

22.1 

39.7 

36 

37 

99.3 

75.7 

61.2 

56.6 

63.3 

82.6 

i6.3 

66.4 

35.6 

27.2 

45.2 

37 

38 

5902.2 

78.8 

64.3 

60.0 

66.8 

86.3 

20.3 

70.7 

4o.3 

32.3 

5o.8 

38 

39 

o5.o 

81.8 

67.5 

63.3 

70.4 

90.1 

24.3 

75.i 

45.o 

37.3 

55.3 

39 

4o 

5907.9 

6084.8 

6270.7 

6466.7 

6673.9 

6893.9 

7128.4 

7379-4 

7649.  7 

7942.4 

8261.9 

4o 

4i 

10.8 

87.8 

73.9 

70.0 

77-4 

97-7 

32.4 

83.7 

54.3 

47.5 

67.5 

4i 

42 

i3.7 

90.8 

77.1 

73.4 

81.0 

6901.5 

36.4 

88.1 

Sg.o 

52.6 

73.1 

42 

43 

16.6 

93.9 

80.2 

76.7 

84-6 

o5.3 

4o.5 

92.4 

63.  7 

57.7 

78.6 

43 

44 

19.4 

96.9 

•83.4 

80.1 

88.2 

09.1 

44.5 

96.8 

68.4 

62.8 

84-3 

44 

45 

22.3 

99.9 

86.6 

83.5 

91.7 

I2.9 

48.6 

74oi.i 

73.2 

68.0 

89.9 

45 

46 

25.2 

6io3.o 

89.8 

86.9 

95.3 

I6.7 

52.7 

o5.5 

77-9 

73.i 

95.5 

46 

47 

28.1 

06.0 

93.0 

90.2 

98.9 

20.  5 

56.7 

09.9 

82.6 

78.2 

83oi.i 

47 

48 

3i.o 

09.0 

96.2 

93.6 

6702.5 

24.3 

60.8 

i4-3 

87.3 

83.4 

06.7 

48 

49 

33.9 

12.  1 

99.4 

97.0 

06.  i 

28.1 

64.9 

18.6 

92.! 

88.5 

12.4 

49 

5o 

5936.8 

6n5.i 

6302.6 

65oo.4 

6709.7 

693i.9 

7i69.o 

7423.0 

•7696.8 

7993-7 

83i8.i 

5o 

5i 

39.7 

18.2 

o5.8 

o3.8 

13.2 

35.7 

73.i 

27.4 

77oi.5 

98.9 

23.8 

5i 

52 

42.6 

21.2 

09.1 

07.2 

16.8 

39.6 

77.2 

3i.8 

o6.3 

8004.0 

29.4 

52 

53 

45.5 

24.3 

12.3 

10.6 

20.4 

43.4 

81.2 

36.2 

n.  i 

09.2 

35.i 

53 

54 

48.4 

27.3 

i5.5 

i4-o 

24.0 

47-2 

85.3 

4o.6 

i5.8 

i4-4 

4o.8 

54 

55 

5i.3 

3o.4 

18.7 

i74 

27.7 

5x.i 

89.5 

45.i 

20.6 

19.6 

46.5 

55 

56 

54.2 

33.4 

21.9 

20.8 

3i.3 

54.9 

93.6 

49-5 

25.4 

24.8 

52.2 

56 

57 

57.2 

36.5 

25.1 

24.2 

34.9 

58.8 

97-7 

53.9 

30.2 

3o.o 

58.o 

57 

58 

60.1 

39.6 

28.4 

27.6 

,  38.5 

62.6 

7201.8 

58.3 

35.o 

35.2 

63.7 

58 

59 

63.o 

42.6 

3i.6 

3i.o 

42.1 

66.5 

o5.9 

62.8 

39.8 

4o.5 

69.4 

59 

CORRECTIONS  TO  MIDDLE  LATITUDE. 


1 

Mid. 
Lat. 

DIFFERENCE  OF  LATITUDE. 

1° 

2D 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

16* 

17° 

18° 

19°  20° 

o 

i5 

0 

2 

3 

5 

7 

9 

12 

i5 

18 

22 

26 

3i 

36 

4i 

47 

52 

59 

65 

72 

16 

o 

2 

3 

4 

6 

II 

i4 

18 

21 

25 

3o 

34 

39 

44 

5o 

56 

62 

69 

17 

o 

2 

3 

4 

6 

8 

II 

i4 

!7 

20 

24 

28 

33 

38 

43 

48 

54 

60 

66 

18 

o 

3 

4 

6 

8 

IO 

i3 

16 

2O 

23 

27 

32 

36 

4i 

46 

52 

58 

64 

I9 

0 

3 

4 

6 

8 

10 

i3 

16 

19 

22 

26 

3o 

35 

4o 

45 

5o 

56 

61 

20 

o 

2 

4 

5 

7 

IO 

12 

i5 

18 

22 

25 

29 

34 

38 

43 

48 

54 

60 

21 

o 

2 

4 

5 

7 

9 

12 

i5 

18 

21 

25 

29 

33 

37 

42 

47 

52 

58 

22  !  o 

2 

4 

5 

7 

9 

12 

i4 

17 

21 

2/1 

28 

32 

36 

4i 

46 

5i 

56 

23 

0 

2 

3 

5 

7 

9 

II 

i4 

I7 

2O 

23 

27 

3i 

35 

4o 

45 

5o 

55 

24 

o 

2 

3 

5 

7 

9 

II 

i4 

16 

20 

23 

27 

3i 

35 

39 

44 

49 

54 

25 

0 

2 

3 

5 

7 

9 

II 

i3 

16 

I9 

23 

26 

3o 

34 

39 

43 

48 

53 

26 

0 

2 

3 

5 

6 

8 

II 

i3 

16 

J9 

22 

26 

3o 

34 

38 

42 

47 

52 

27 

o 

2 

3 

5 

6 

8 

II 

i3 

16 

19 

22 

25 

29 

33 

37 

42 

47 

52 

28 

o 

2 

3 

5 

6 

8 

10 

i3 

16 

18 

22 

25 

29 

33 

37 

4i 

46 

5i 

29 

0 

2 

3 

5 

6 

8 

10 

i3 

i5 

18 

21 

25 

28 

32 

37 

4i 

46 

5i 

3o 

o 

2 

3 

5 

6 

8 

IO 

i3 

i5 

18 

21 

25 

28 

32 

36 

4i 

45 

5o 

3i 

o 

2 

3 

5 

6 

8 

IO 

12 

i5 

18 

21 

24 

28 

32 

36 

4o 

45 

5o 

32 

o 

o 

2 

3 

4 

6 

8 

IO 

12 

i5 

18 

21 

24 

28 

32 

36 

4o 

45 

5o 

33 

0 

o 

2 

3 

4 

6 

8 

10 

12 

i5 

18 

21 

24 

28 

32 

36 

4o 

45 

49 

34 

o 

o 

2 

3 

4 

6 

8 

IO 

12 

i5 

18 

21 

24 

28 

32 

36 

4o 

45 

49! 

35 

o 

0 

2 

3 

4 

6 

8 

IO 

12 

i5 

18 

21 

24 

28 

32 

36 

4o 

45 

49 

36 

o 

2 

3 

4 

6 

8 

IO 

12 

i5 

18 

21 

24 

28 

32 

36 

4o 

45 

49 

37 

o 

2 

3 

4 

6 

8 

10 

12 

i5 

18 

21 

24 

28 

32 

36 

4o 

45 

49 

38 

0 

2 

3 

4 

6 

8 

IO 

12 

i5 

18 

21 

24 

28 

32 

36 

4o 

45 

5o 

39 

o 

2 

3 

4 

6 

8 

IO 

12 

i5 

18 

21 

24 

28 

32 

36 

4o 

45 

5o 

4o 

o 

2 

3 

5 

6 

8 

IO 

i3 

i5 

18 

21 

25 

28 

32 

36 

4i 

45 

5o 

4i 

0 

2 

3 

5 

6 

8 

IO 

i3 

i5 

18 

21 

25 

28 

32 

37 

4i 

46 

5i  j 

42 

o 

2 

3 

5 

6 

8 

IO 

i3 

i5 

18 

22 

25 

20 

33 

37 

4i 

46 

5i  i 

43 

o 

2 

3 

5 

6 

8 

IO 

i3 

16 

18 

22 

25 

29 

33 

37 

42 

46 

52 

44 

0 

2 

3 

5 

6 

8 

IO 

i3 

16 

J9 

22 

25 

20 

33 

38 

42 

47 

52 

45 

o 

2 

3 

5 

6 

8 

II 

i3 

16 

I9 

22 

26 

3o 

34 

38 

43 

48 

53 

46 

o 

2 

3 

5 

6 

8 

II 

i3 

16 

I9 

22 

26 

3o 

34 

38 

43 

48 

53 

47 

0 

2 

3 

5 

7 

9 

II 

i3 

16 

23 

26 

3o 

35 

39 

44 

49 

54 

48 

o 

2 

3 

5 

7 

9 

II 

i4 

17 

20 

23 

27 

3i 

35 

4o 

44 

5o 

55 

*9 

o 

2 

3 

5 

7 

9 

II 

i4 

17 

20 

23 

27 

3i 

36 

4o 

45 

5o 

56 

5o 

o 

9 

4 

5 

7 

9 

II 

i4 

20 

24 

28 

32 

36 

4i 

46 

5i 

57 

5i 

0 

2 

4 

5 

7 

9 

12 

i4 

17 

21 

24 

28 

32 

37 

42 

47 

52 

58 

52 

b 

2 

4 

5 

7 

9 

12 

i5 

18 

21 

25 

29 

33 

38 

43 

48 

53 

59 

53 

o 

2 

4 

5 

7 

IO 

12 

i5 

18 

21 

25 

29 

34 

38 

43 

49 

54 

60 

54 

o 

2 

4 

5 

7 

10 

12 

i5 

18 

22 

26 

3o 

34 

39 

44 

5o 

56 

62 

55   o 

2 

4 

6 

8 

IO 

i3 

16 

19 

22 

26 

3i 

35 

4o 

45 

5i 

57 

63 

56 

o 

3 

4 

6 

8 

IO 

i3 

16 

!9 

23 

27 

3i 

36 

4i 

46 

52 

58 

65 

57 

o 

3 

4 

6 

8 

10 

i3 

16 

20 

24 

28 

32 

37 

42 

48 

54 

60 

66 

58 

0 

2 

3 

4 

6 

8 

II 

i4 

17 

20 

24 

28 

33 

38 

43 

49 

55 

61 

68 

59 

0 

2 

3 

4 

6 

8 

II 

i4 

21 

25 

29 

34 

39 

45 

5o 

57 

63 

70 

60 

o 

2 

3 

4 

6 

9 

II 

i4 

18 

22 

26 

3o 

35 

4o 

46 

52 

58 

65 

72 

61 

o 

2 

3 

5 

7 

9 

12 

i5 

18 

22 

26 

3i 

36 

42 

47 

53 

60 

67 

75 

62 

o 

2 

3 

5 

7 

9 

12 

i5 

19 

23 

27 

32 

37 

43 

49 

55 

62 

7° 

77 

63 

0 

2 

3 

5 

7 

10 

12 

16 

20 

24 

28 

33 

39 

44 

5i 

57 

64 

72 

80 

64 

o 

2 

3 

5 

7 

10 

13 

16 

20 

24 

29 

34 

4o 

46 

52 

59 

67 

75 

83 

65 

o 

2 

3 

5 

7 

IO 

i3 

I? 

21 

25 

3o 

36 

4i 

48 

54 

62 

69 

78 

86 

66 

0 

2 

3 

5 

8 

II 

i4 

18 

22 

26 

32 

37 

43 

5o 

57 

64 

72 

81 

9° 

67 

o 

2 

4 

6 

8 

II 

i4 

18 

23 

28 

33 

39 

45 

52 

59 

67 

76 

85 

94 

68 

0 

2 

4 

6 

8 

12 

i5 

19 

24 

29 

34 

4o 

47 

54 

62 

70 

79 

89 

99 

69 

o 

2 

4 

6 

9 

12 

16 

20 

25 

3o 

36 

42 

49 

57 

65 

74 

83 

93 

io4 

70 

0 

.  2 

4 

6 

9 

13 

16 

21 

26 

32 

38 

44 

52 

60 

68 

78 

88 

98 

no 

o 

2 

4 

7 

10 

i3 

17 

22 

27 

33 

4o 

47 

55 

63 

72 

82 

93 

io4 

116 

72 

o 

3 

5 

7 

IO 

i4 

18 

23 

29 

35 

42 

49 

58 

67 

76 

87 

98  in 

124 

150      LOGARITHMS   FOR   COMPUTING   COMPOUND   INTEREST. 


In  computing  compound  inter*  st  for  long  periods  of  time, 
the  following  logarithms  to  more  than  six  places. 

it  is  necessary  to  have 

Number. 

Logarithm. 

Number. 

Logarithm. 

.0026 
.0060 
.0076 

.0100 

.0126 
.0160 
.0176 
.0200 
.0226 
.0260 
.0276 
,o3oo 
,o325 
.o35o 
.P375 
,o4oo 

.00108  438i3 
.00216  60618 
.oo324  5o548 

.00432  13738 

.00639  60319 
.00646  60422 
.00763  44i79 
.00860  01718 
.00966  33167 
.01072  38654 
.01178  i83o5 
.01283  72247 
.01389  oo6o3 
.01494  03498 
.01698  81064 
.01703  33393 

.0426 
.o45o 
.0475 
.0600 
.0626 
.0660 
.0676 
.0600 
.0626 
.0660 
.0676 
.0700 
.0726 
.0760 
.0776 
.0800 

,01807  6o636 
.01911  62904 
.020i5'4o3i6 
.02118  92991 
.02222  21046 
.02326  24696 
.02428  03760 
.O253o  58653 
.02632  89387 
.02734  96078 
.0283678837 
.0293837777 
.o3o39  73009 
.o3i4o  84643 
.o324i  72788 
.o3342  37555 

NUMBERS  OFTEN  USED  IN  CALCULATIONS. 

Circumference  < 
Surface  of  a  spl 
Area  of  a  circle 
Area  of  a  circle 
Capacity  of  a  s[ 
Capacity  of  a  sp 
1  —  3.1416926  . 

)f  a  circle  to  diameter  i  } 
lere  to  diameter  i           > 

3.1416926 

.7863982 
.6236988 
4.1887902 
0.3183099 
°.  2967796 
206264".  8 
.0174533 
.0002909 
.00000486 
.00000970 
.ooooi454 
.00001939 
.00002424 
.00002909 
.00003394 
.00003879 
.oooo4363 
2.7182818 
.4342945 
1296000 
864oo 
6280 

Logarithms. 
0.497l5o 

9.896090 
9.718999 
0.622089 
9.602860 

i.758i23 
5.3i4425 
8.241877 
6.463726 
4.686676 
4.986606 
6.162696 
5.287635 
5.384545 
5.463726 
5.53o673 
5.588665 
6.639817 
0.434294 
9-637784 
6.  112606 
4.9365i4 
3.722634 

to  radius  i       ....     --) 

to  diameter  i 

>here  to  diameter  i 

_ 

>here  to  radius  i  



Arc  equal  to  rac 
Arc  equal  to  raci 
Length  of  i  deg 
Length  of  i  mit 
Sine  of  i  secon 
Sine  of  2  secon< 
Sine  of  3  secon 
Sine  of  4  secon 
Sine  of  5  secon 
Sine  of  6  secon 
Sine  of  7  secon 
Sine  of  8  secon 
Sine  of  9  secon 
Base  of  Napier 
Modulus  of  the 
36o  degrees  ex 
24  hours  expre 
Number  of  feet 

ius  expressed  in  degrees 
ius  expressed  in  seconds 
ree  in  parts  of  radius  

—  5i 

mte  in  parts  of  radius 

^ 

i  

Is  

3s  



is  

3s  

3s  

3s  

•     " 

3s  

3s  

s  system  of  logarithms.  .  . 

common  logarithms  .  . 

pressed  in  seconds.  . 

5sed  in  seconds  

in  one  mile  

THE 

END. 

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L  O  O  M  I  S'S 


SERIES    OF    SCHOOL    AND    COLLEGE 

TEXT-BOOKS. 


THE  Course  of  Mathematics  by  Professor  Loomis  has  now  been  for  several  years  before  th« 
Public,  and  has  received  the  general  approbation  of  Teachers  throughout  the  country.  The  fol- 
lowing are  some  of  the  Institutions  in  which  this  Course  has  been  introduced,  either  wholly  or 
in  part:  Dartmouth  College,  N.  H. ;  "Williams  College,' Mass. ;  Amherst  College,  Mass. ;  Trin- 
ity College,  Conn. ;  Wesleyan  University,  Conn. ;  Hamilton  College,  N.  Y. ;  Hobart  Free  Col- 
lege, N.  Y. ;  New  York  University,  N.  Y. ;  Dickinson  College,  Penn. ;  Jefferson  College,  Penn. ; 
Alleghany  College,  Penn. ;  Lafayette  College,  Penn. ;  St.  James's  College,  Md. ;  Emory  and 
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ana College,  La. ;  Transylvania  University,  Ky. ;  Cumberland  College,  Ky. ;  Western  Keserve, 
College,  Ohio ;  Marietta  College,  Ohio ;  Oberlin  College,  Ohio ;  Antioch  College,  Ohio ;  As- 
bury  University,  Ind. ;  Wabash  College,  Ind. ;  Illinois  College,  111. ;  Shurtleif  College,  111. ; 
M'Kendree  College,  HI. ;  Knox  College,  111. ;  Missouri  University,  Mo. ;  University  of  Michigan, 
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Professor  Loomis's  text-books  are  distinguished  by  simplicity,  neatness,  and  accuracy;  and  are  remarkably  well 
adapted  for  recitation  in  schools  and  colleges.  I  am  satisfied  no  books  in  use,  either  in  America  or  England,  are 
so  well  adapted  to  the  circumstances  and  wants  of  American  teachers  and  pupils. — W.  C.  LAEEABEE,  late  Professor 
of  Mathematics,  Indiana  Asbury  University. 

A  Treatise  on  Algebra. 

Eighteenth  Edition.     8vo,  359  pages,  Sheep 
extra,  $1  00. 

This  treatise  is  designed  to  contain  as  much  of  algebra 
as  can  be  profitably  read  in  the  time  allotted  to  this  study 
in  most  of  our  colleges,  and  those  subjects  have  been  se- 
lected which  are  most  important  in  a  course  of  mathe- 
matical study.  Particular  pains  have  been  taken  to  cul- 
tivate in  the  mind  of  the  student  a  habit  of  generaliza- 
tion, and  to  lead  him  to  reduce  every  principle  to  its 
most  general  form.  It  is  believed  that,  in  respect  of  dif- 
ficulty, this  treatise  need  not  discourage  any  youth  of  fif- 
teen years  of  age  who  possesses  average  abilities,  while 
it  is  designed  to  form  close  habits  of  reasoning,  and  cul- 
tivate a  truly  philosophical  spirit  in  more  mature  minds. 
In  accordance  with  the  expressed  wish  of  many  teachers, 
a  classified  collection  of  two  hundred  and  fifty  problems 
is  appended  to  the  last  edition  of  this  work. 

Professor  Loomis's  Algebra  is  peculiarly  well  adapted 
to  the  wants  of  students  in  academies  and  colleges.  The 
materials  are  well  selected  and  well  arranged ;  the  rules 
and  principles  are  stated  with  clearness  and  precision, 
and  accompanied  with  satisfactory  proofs,  illustrations, 
and  examples.— A.  D.  STANLEY,  late  Professor  of  Mathe- 
matics in  Yale  College. 


A  Treatise  on  Arithmetic, 

Theoretical  and  Practical.     12mo,  352  pages, 

Sheep  extra,  75  cents. 

This  volume  explains,  in  a  simple  and  philosophical 
manner,  the  theory  of  all  the  ordinary  operations  of 
Arithmetic,  and  illustrates  them  by  examples  sufficient- 
ly numerous  to  impress  them  indelibly  upon  the  mind  of 
the  pupil.  It  is  designed  for  the  use  of  advanced  stu- 
dents in  our  public  schools,  and  furnishes  a  complete 
preparation  for  the  study  of  Algebra,  as  well  as  for  the 
practical  duties  of  the  counting-house. 

The  answers  to  about  one  third  of  the  questions  are 
given  in  the  body  of  the  work ;  but,  in  order  to  lead  the 
student  to  rely  upon  his  own  judgment,  the  answers  to 
the  remaining  questions  are  purposely  omitted.  For  the 
convenience,  however,  of  such  teachers  as  may  desire  it, 
there  is  published  a  small  edition  containing  all  the  an- 
swers to  the  questions. 

Elements  of  Algebra. 

Designed  for  the  Use  of  Beginners.     Twelfth 

Edition.     12mo,  281  pages,  Sheep  extra,  62§- 

cents. 

This  volume  is  intended  for  the  use  of  students  who 
have  just  completed  the  study  of.  Arithmetic.  It  is  be- 
lieved that  it  will  be  found  sufficiently  clear  and  simple 
to  be  adapted  to  the  wants  of  a  large  class  of  students  in 
our  common  schools.  It  explains  the  method  of  solving 
equations  of  the  first  degree,  with  one,  two,  or  more  un- 
known quantities  ;  the  principles  of  involution  and  of 
evolution ;  the  solution  of  equations  of  the  second  de- 
gree ;  the  principles  of  ratio  and  proportion,  with  arith- 
metical and  geometrical  progression.  Every  principle 
is  illustrated  by  a  copious  collection  of  examples ;  and 
two  hundred  miscellaneous  problems  will  be  found  at  the 
close  of  the  book. 

I  have  used  Loomis's  Elements  of  Algebra  in  my  school 
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gree to  give  the  pupil  a  clear  and  comprehensive  knowl- 
edge of  the  elements  of  the  science.  I  believe  teachers 
of  Academies  and  High  Schools  will  find  it  all  that  they 
can  desire  as  a  text-book  on  this  branch  of  Mathematics. 
—Professor  ALONZO  GRAY,  Brooklyn  Heights  Seminary. 


Elements  of  Geometry  and  Conic  Sec- 
tions. 

Fifteenth  Edition.    8vo,  234  pages,  Sheep 

extra,  75  cents. 

The  arrangement  of  the  propositions  in  this  treatise  is 
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the  model  of  Euclid.  The  propositions  are  all  enunciated 
in  general  terms,  with  the  utmost  brevity  which  is  con- 
sistent with  clearness.  The  short  treatise  on  Conic  Sec- 
tions appended  to  this  volume  is  designed  particularly 
for  those  who  have  not  time  or  inclination  for  the  study 
of  analytical  geometry.  The  last  edition  of  this  work 
contains  a  collection  of  theorems  without  demonstrations, 
and  problems  without  solutions,  for  the  exercise  of  the 
pupiL 


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ELEMENTS  OF  NATURAL  PHILOSOPHY, 

DESIGNED   FOE 

ACADEMIES  AND  HIGH  SCHOOLS. 

By    Elias    Loomis,    LL.D. 

12mo,  350  pages,  Sheep  extra,  $1  00. 

This  volume  is  the  result  of  many  years  of  laborious  study,  and  presents  in  an  elementary  form  the  fruits  of 
much  research.  It  is  designed  particularly  for  the  use  of  the  higher  classes  in  Academies  and  High  Schools,  and 
its  primary  object  is  to  cultivate  the  habit  of  philosophical  reflection  and  observation. 

The  following  are  a  few  of  the  Notices  of  LOOMIS'S  NATCRAL  PHILOSOPHY  which  have  been  re- 
ceived by  the  Publishers  : 

Prof.  Loomis's  Elements  of  Natural  Philosophy  is  one 
of  the  best  and  most  complete  works  of  the  kind  that  has 


been  published,  and  possesses  a  clearness  and  conciseness 
seldom  equaled.  I  have  seldom  seen  so  much  useful  in- 
formation in  one  volume.— EDWARD  T.  FBISTOB,  Profes- 
sor of  Mathematics,  Columbian  College,  D.  C. 

This  volume  has  the  merit  of  being  a  digest  and  not  a 
compilation.  For  a  large  class  of  students  it  is  the  only 
suitable  work  on  this  subject  that  I  have  seen,  bringing 
into  use,  as  it  does,  all  the  mathematics  usually  studied 
in  our  academies,  and  no  more.— E.  W.  EVANS,  Profes- 
sor of  Natural  Philosophy  in  Marietta  College,  Ohio. 

Prof.  Loomis's  Natural  Philosophy  is  clear,  accurate, 
and  methodical.— DANIEL  KIBKWOOD,  Prof essor  of  Nat- 
ural Philosophy  in  Indiana  State  University. 

The  characteristics  of  Loomis's  Mathematical  Work*, 
which  we  so  highly  prize,  are  fully  sustained  in  his  Nat- 
ural Philosophy.  I  am  glad  to  find  at  last  a  text-book 
on  this  subject  so  logically  expressed,  so  complete  and  so 
accurate.— N.  B.  WEBSTER,  A.M.,  President  of  Virginia 
Collegiate  Institute,  Portsmouth,  Va. 

This  work  of  Prof.  Loomis  claims  to  be  a  philosoph- 
ical treatise.  For  clearness  of  style  and  fullness  of  illus- 
tration we  have  not  met  its  equal.  Adapted  to  the  high- 
er classes  in  academies  and  high  schools  where  mathe- 
matics have  been  pursued  only  through  plane  trigonome- 
try, it  is  ready  at  all  times  to  give  a  reason  for  a  phenom- 
enon, while  the  numerous  references  to  the  every-day  oc- 
currences of  life  make  it  exceedingly  interesting  to  those 
who  do  not  care  for  demonstrations.  We  hope  it  will 
crowd  out  of  our  schools  the  heterogeneous  productions 
that  school  boys  have  to  stuff  themselves  with ;  and  thus 
give  thorough  instruction  that  will  tend  to  develop  some 
faculties  besides  memory.  —  S,  J.  C.  SWEZEY,  Marion, 
Alabama. 

Prof.  Loomis's  Natural  Philosophy  combines  concise- 
ness with  very  great  clearness  of  illustration,  and  is  the 
best  text-book  of  the  kind  that  I  have  examined.— Prof. 
W.  FEEBEL,  Nashville,  Tenn. 

Prof.  Loomis's  treatise  has  my  decided  preference  as  a 
text-book  on  Natural  Philosopy.  It  is  simple  and  com- 
prehensive in  its  style,  and  its  principles  are  discussed 
with  clearness  and  brevity. — J.  W.  FERREE,  A.M.,  Pro- 
fessor of  Mathematics,  Dickinson  Seminary,  Pa. 

Prof.  Loomis's  Natural  Philosophy  is  the  best  elemen- 
tary work  on  this  subject  which  I  have  hitherto  seen.  It 


treats  is  pregnant  with  useful  knowledge.— A.  W.  MASON, 
Jeansville,  Penn. 


Prof.  Loomis's  Natural  Philosophy  is  the  best  text- 
book on  that  subject  yet  published.  With  all  its  value 
as  a  text-book,  it  combines  a  pleasing  style,  instructive 
examples  and  illustrations,  and  is  quite  a  readable  book 
for  others  besides  school-boys.— B.  W.  MoDorraoLD, 
Professor  in  Bethel  College,  Tenn. 

While  this  volume  requires  of  the  pupil  nothing  be- 
yond a  knowledge  of  the  elementary  mathematics,  it  de- 
velops the  philosophy  of  all  the  leading  principles  of  me- 
chanics and  physics.  Its  definitions  are  clear  and  con- 
cise, its  statement  of  principles  methodical  and  accurate. 
It  embraces  in  a  duodecimo  volume  of  350  pages,  a  com- 
plete digest  of  what  is  usually  spread  over  three  or  four 
times  this  space.  Nor  by  this  condensation  is  the  study* 
rendered  repulsive,  but  exactly  the  reverse.  We  com- 
mend this  work  without  qualification,  as  one  admirably 
adapted  to  interest  the  pupil,  while  it  cultivates  the  habit 
of  philosophical  reflection  and  observation. — New  York 
Observer. 

This  volume  is  not  only  an  admirable  treatise  for  the 
use  of  the  higher  classes  in  schools,  but  is  a  most  conve- 
nient compendium  of  the  latest  discoveries  in  Natural 
Philosophy  for  the  instruction  of  adult  readers. — New 
York  Commercial  Advertiser. 

This  volume  is  an  admirable  compendium  of  the  prin- 
ciples of  Natural  Philosophy;  yet,  strange  to  say,  it  is 
not  dull,  heavy,  or  incomprehensible,  bir 
terms  that  all  can  comprehend,  and  that  few  will  be  una- 
ble to  remember.— Baltimore  Dailii  7V 

Among  the  numerous  books  of  its  class  which  have 
originated  in  this  country,  this  volume  has  no  superior 
in  clearness,  accuracy,  and  comprehensiveness. — Boston 
Courier. 

Prof.  Loomis's  works  on  Arithmetic,  Geometry,  &c., ' 
are  models  of  clear  and  precise  style,  comprehensive 
definitions,  and  accurate  language.  This  work  on  Nat- 
ural Philosophy  is  marked  by  the  same  excellences. — To- 
ronto Globe. 

Ten  pages  of  this  book,  which  may  easily  be  read  by 
every  mechanic  in  his  winter  evenings,  will  FO  fill  his 
head,  as  to  leave  no  room  for  idle  thoughts. — Newark 
Daily  Advertiser. 

The  study  of  Prof.  Loomis's  work  will  make  solid 
thinkers,  not  smatterers.  While  popularizing  science, 


is  not  only  fitted  for  high  schools,  but  is  a  perfect  treas-    he  has  not  frittered  away  the  solidity  and  accuracy  which 
ure  to  the  private  student.     Every  subject  on  which  it  |  alone  give  it  a  title  to  that  name. — a,  Y.  Daily  Ni 


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Published  by  HARPER  &  BROTHERS,  Franklin  Square,  N,  Y, 


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